My advice to any novice tool buyers who are actually planning on using their tools with some regularity. Buy the absolute best you can especially the basic stuff like Allen keys/wrenches and a good torque wrench and JIS (not Phillips because JIS will work with both and not cam out like Phillips) and other screwdrivers (flat head), a good set of cable cutters and a good chain tool. Those will do much of the basic stuff you will need and the better you get the longer it will last and the less chance you will have of stripping things out or getting poor cuts or something like that.
Here are my top recommendations if you can swing it
Silca HX-Three Allen key Set or
PB Swiss Rainbow set or
Pedro's L Wrench Set.
Make sure though if getting a ball end set that you aren't tightening down fully or loosening from tight using the ball end as you can strip a bolt head
Park T25 Sliding T-Handle Torx Wrench
If you have no other Torx bits on your bike then invest in a good quality T25 if you do have others
Park TWS-1 set will do you well but I still might go with that new Sliding T-Handle wrench for the T25 as that is most common and should make installing a 6 bolt disc rotor more of a breeze
Park DSD-2 or Vessel Megadora #2
Both will work on Phillips head stuff without camming out
Jagwire Pro Housing Cutter
Though I would also recommend the Knipex one and for budget the Park or Pedro's one will do the job especially if not using it all the time carelessly.
I went ahead and went full ****** and got the
Decade Chain Tool from Abbey, you probably shouldn't do that unless you are truly serious. It is not a cheap tool in any sense of the word and is for a true tool enthusiast who will use it.
For me the
Park CT 3.3 would do just fine for a home mechanic. Just be careful and if you feel it binding back off so you don't break a pin and certainly order plenty of extra pins but so far I think I broke one chain pin that had been heavily used in a shop environment and I was a bit more careless that time. If you take your time and make sure everything is going in straight and true you are much less likely to break the pin.
Park ST-3
This one is great for 8-9-10 sockets which can be common on fenders older/cheap brakes (nutted) and some racks as well. Personally I would get a good high quality bit and driver (Snap-On here's looking at you) because I find ratcheting stuff easier to work with.
Park ATD-1.2
Properly torquing bolts is always important as you can ruin expensive parts easily. This tool has some adjustability but not as much as a higher end one will have but for a beginner I found this one perfect for most things. If I could swing it right now I would own a Snap-On Digital one those are beyond nice, my boss has two and getting to use them is a dream to say the least.
My favorite on the bike tools are:
Crank Brothers M10
Good long tools, with most everything you will need and in fun colors. I own a bunch of these
Spurcycle Tool
Small bits can be a pain but the tool is really nice to use on the road and it is not heavy
Pedro's Trixie
If you ride a fixed gear bike this would be the tool to have
For general bike tools Park Tool, Pedro's, Hozan and Unior make fairly good quality tools and you are less likely to go wrong with those. I generally avoid any pre-made kits as I would want to change stuff out right away or over time so it is wasted money. I can get a box or tool wrap easy enough and then fill it as needed. Again though buy the best stuff you can if you truly plan on working with tools. Also don't be rough with things, be careful and precise and you are less likely to cause damage and of course always ask questions when you are stuck.
I see way too often young mechanics thinking they have a problem they have never encountered solved and then they end up breaking something or stripping a bolt and they have a costly mistake on their hands. Check with your local long time mechanic (some appreciate beer/alcohol or baked goods or greens or maybe other things) Chances are they have seen it and if you don't have a local shop or are agoraphobic Park Tool has great videos, Zinn and the Art of ______ Bike Maintenence (road, mountain, tri) is excellent as is Sheldon Brown (who is a true legend and sorely missed in the cycling and mechanics community).
If you are truing wheels often get a decent truing stand and find your favorite truing key everyone is a bit different on what their fingers like. If you don't have a truing stand and knowledge on truing wheels you might leave it to the professionals or practice on a cheap wheel you won't be riding on.
Gerd Schraner's The Art of Wheelbuilidng is a good resource even if poorly put together in that PDF.