I have a CCM falcon mountain bike. It needs new brakes (Entire set, cables, pads, etc.) and new gears (mainly cables but probably shift too.).
Would it be cheaper for me to fix the bike or go out and by another bike, which would be a bmx bike? Thanks for your help!

Well, it seems to be a $150 bike per a quick search. My guess is a new bike. However, if it is just cables, you can replace those for not much money.

Good USED MTBs are readily available, for very little $$. Now if it is just a few cables, you are talking a $5 fix, and I would certainly do that first.

WIth all due respect, you don't strike me as a person with the knowhow to install and adjust a completely new cantilever or V-brake set. Brakes are a thing it's best not to make mistakes on.

BL

You need to assess the bike as a whole to determine if it is something worth putting money into. It appears that the CCM Falcon is a department store bike that goes for under $150 new. Brake pads and cables are part of routine maintenance and you can expect to replace them on any well used bike. But if you are talking about replacing the brake mechanisms, the freewheel (rear "gears"), chainrings/crankset (front "gears") and/or shifters there is no way you can come out well starting with a department store bike. If you are looking at putting $150 or so into a bike, I would suggest you sell, part out, or donate the one you have; stay away from WalMart level bikes; and put your money into a used higher quality bike that is in decent shape and doesn't need any major work. The safest way to do this is to go to a reputable local bike shop (a real bike shop, not just a store that sells bikes) and tell them what you want in a bike. If you have more experience and know what to look for and watch out for in a used bike, then you can make some good deals from private sellers on Craigs List, garage sales, etc. but it can take some hunting and you have to have the judgement and patience to wait for "the right one". I've found it effective to place a "wanted to buy" in CL as potential sellers usually check out the list before posting their bikes for sale.

Cable replacement, combined with new brake pads and adjustment of both the brakes and derailleurs will get rid of a lot of problems. Usually there's no need to go replacing anything else unless something's actually broken.

Or make them worse if you don't do it correctly.

When you say new brakes and gears are you talking about serious hardware like the brake calipers or levers, and the derailleurs, of only normal replacement items like the cables and brake shoes?

It's a big difference, because cables and shoes are fairly cheap whereas if you need more it'll take it out of range.

See if there's a local bike co-op or non-profit repair shop where they can do basic repairs inexpensively, and get a quote for the least you need. Also have them review what else is needed or soon will be like wheel alignment, tires, etc. When you have a handle of the total cost of getting this back on the road, compare that to the BMX bike, or mtn. bike options. Note that you're comparing to a used bike, these often need exactly what you need, cables, brake shoes, tires, and adjustments, so make sure to know the total cost there too.

sorry I didn't mention this before, but I will be paying a bike repair shop to get the parts and install them for me.

BMX bike

Go to the bike repair shop, without your bike, and tell them what kind of riding you want to do. Then ask about used bikes. As mentioned before, brake pads and cables are an easy fix, but I wouldn't even consider paying someone to do major repairs on a department store bike. Once you start tearing into a low end bike, it's like opening a can of worms and soon you can have far more into it than it's worth. It sounds like you want a BMX bike anyway, so sock money away for that rather than putting it into repairs on a bike that is your second choice anyway.

If I recall the CCM Falcon, it's like a BSO in the style of Mtn Bike, with some pseudo suspension. There at three things about the brakes that drive me nuts on this bike and the Canucks, which are more avant garde on consumer product safety should outlaw plastic spring tension cams on V-brakes. There should only be metal cams or they must pass some hugely rigorous tests which real bikers get to oversee. Needless to say, none of the CCM bikes that that spec those ultra-cheap V-brake-looking brakes can stay centered on the rims. Next thing that drives me nuts is the use of corrosion-promoting metals for the brake noodle. Of the neighbourhood up in Canada where I vacation, there used to be just 4 households with kids in 60 units. Every kid that had a CCM bike had a rusty or broken V-brake noodle. It got to the point where I'd see the kids riding with a missing critical brake because the noodle had rusted through. For God's sake... it's the north... like Vancouver. It rains more than 170 days a year here. There's humidity and our community is right next to a big Salt Water estuary ... aka Howe Sound. Duh... So I stock a bunch of brake noodles. Stainless or alloy. 90 deg and 115 deg curvature. Lastly, you have to wonder just how cheap the brake shoes are on these brakes. I thought my bulk buy for threaded post ATB style/Vbrk shoes at $3/pr was darn low and they work pretty well. But whatever is on these are even cheaper. Noisy, flimsy, easily corrodes, can't hold toe-in, and a host of other points that make them so bad, I stock a bag of bulk brake shoes for the kids. Why? Because their grandmas and grandpas up in that retirement community aren't the handiest folks with mechanical things, and the few actually young households there are a bunch of wealthy sales guys who get manicures and can't stoop low enough to even pick up a twooney if they saw it on the ground. (Needless to say, they like it when I'm up visiting - I save them thousands in electronics and HVAC repairs.... that story for a different forum).

Back to the OP's issue. What's the bike cost? About $130 on sale plus tax? If you went out, you'd have to pay about $300+ to get some decent brakes with metal spring tension cams. On the otherhand, a 5 mm allen bolt, a little grease, a rag, and philips screwdriver, and you could spend around $30 mail-order and get a set of front/rear Shimano Acera V-brakes. Then $15 more for some Tektro 316AG levers, $5 for a pair of brake cables, and you're good to go on the brakes. That's $50 for brakes that will serve you extremely well - or at least blow your mind away compared to how bad the older brakes used to be.

To fix your shifting, I'd advise simply looking at the cable routing. 70% of the time, get that housing routed correctly and to the right length solves the problem. 29% of the other time, make sure the factory or whomever installed the derailleurs routed the cable correctly through the plate that the pinch bolt tightens around. Because not lining that up in the proper groove of that plate means the pull angle and length are all wrong and so is the moment arm of your derailleur. If you are part of that nasty 1% and must replace shifters, you probably suffer from one of two choices CCM makes - the cheapest plastic thumb shifters ever invented... (until next year... then they'll be even crappier and cheaper still), or you have the cheapest grip shifts on the planet. You can order online some SRAM MRX Comp (Shimano compatible) 7 speed grip shifts with cables in a box set (left and right) for under $20 CDN. These actually work okay. And get the "micro shifting left" - don't get an indexed left shifter as you'll never get the FD cage alignment correct and the cable pull right to get the indexing to never rub. So just avoid it and use micro-clicks and friction on the left side.

That's $50 - $70 to improve braking and shifting. If you must replace the derailleurs and drive train, then you've passed the threshold of sensible economics (which you probably already did by buying this CCM bike or taking ownership of it in the first place...but that's a different thread...). No. It's not cheap relative to the bike, but you're doing this expos facto, and so it's not as cheap as if the manufacturer has simply spec'd the right thing to start with. Sometimes this saving of $0.50 on a bike is foolish. It just tarnishes the brand and invites the ignorant to keep buying. It truly aspires to the PT Barnum philosophy of a sucker is born every... [insert time interval]. But that's your situation. You have to make some type of decision. The logical one would probably be to start fresh and get a bike of quality that costs considerably more, maybe 5X and then ride and maintain that. It's likely to be far cheaper in the long.

BSO = Throw away when you face extensive mechanical issues, particularly if you pay someone to do the work.