I bought a cheap fixed gear bike (not a Pure Fix, but similar), and plan to slowly upgrade it as I can afford to. My first purchase was a new saddle because the stock one was extremely uncomfortable.

I want to start with areas of the bike I will get the most bang for my buck. Where will I most notice my upgrades?

Saddle - check

I'd start looking at bars/tape and pedals.

But since you got a cheap bike to begin with, maybe make that a beater bike and start saving for a higher quality bike.

Saddle, tires and then put all that cash into a piggy bank for a completely better bike. Replace parts as they wear out, any upgrades for the sake of improved performance are going to generally be a waste of money.

If you do insist, probably the wheels.

Seat, bars, pedals...then replace stuff that breaks, wears out or just plain looks cheesy. eventually you will have all the parts you want on a new bike and then you just have to buy a new Frame/fork

my idea is to slowly turn this into a new higher quality bike. but in the meantime at least have something to ride. ideally i'd like to end up with no original parts. or at least very few.

Wheels and tires...

$$$

Then I'd consider getting parts that you can eventually move over to the next bike you get.

Upgrading a "insert cheap bike here" will make it nicer sure, but it will still be a "insert cheap bike here".

I'm surprised to be hearing bars a lot. For the weight factor, material or shape?

Well it really depends on your riding preferences. If it comes stock with track drops, you probably want to switch them out asap. Or maybe it's a short distance bike and you only want risers on there, or you're going long distances and want some road drops.

The good thing is solid bars don't cost that much and should last forever.

Cheap bikes skip out on bearings. I'd upgrade the bottom bracket, pedals, and wheels/tires

Well, that's the most expensive way to do it.

I bought the best complete bike I could afford. I'm all ears for suggestions on how to save $

Buy a nice fixie helmet first.

I'm beginning to notice that.

as always there are 290381 threads about upgrading low cost bikes and we always say that you should only upgrade when a part wears out, break or feel uncomfortable. That's the best bang for your buck.

Unless it is the brakes that brake. In which case they are doing their job.

Oops

Wheels, tires, and BB would be the best starting points.

If I got a cheap bike I'd probably replace saddle and pedals immediately. Maybe bars too if stocker bars really sucked bad. I might replace tires when I got the dough, keep stock tires as backup.

Upgrade what's broken, uncomfortable, or close to breaking. Otherwise ride your bike and enjoy life.

This. You can start with switching things to sealed cartridge bearing components.

Seems a bit overly complicated for what should just be 'simple upgrades'. Labor costs at shops will be roughly equal to the parts being upgraded (and I doubt OP has the necessary tools for this himself). Personal recommendation, upgrade the saddle, then pedals and bars to suit what you think is comfortable. Then ride the **** out of it. If you'd like a nicer bike, buy/build one and use what you've learned from this before wasting your money.

Nothing complicated about upgrading parts that are loose ball bearing (most likely) to sealed cartridge bearing components. Take it to lbs, buy component, pay small installation fee. Upgrading a saddle is a lot more complicated (if you want to put it that way) because you actually have to find one that you like and fit.

I see your point there. I'm fully imagining that the OP has a Thruster at this point, trying to spare the unnecessary agony of spunking cash into a cheap bike on parts you can't take with you onto another build