Your questions all have the answer: "it depends".
Do you have more time than money? If the answer to that is 'yes' then you should continue to consider making your own XLR cables. But do not stop with XLRs, also make TRS to XLR male, TRS to XLR female and TRS to TRS.
Will store bought or home made cables sound better? If you use high quality cable, good connectors AND your solder does not suck, then the ones you make should sound no worse (and no better) than the best you can buy. Skimp on any of those three things and then a high quality store bought cable will probably exceed the quality of what you make yourself.
Is it cheaper to make them yourself? Well, if you have more time than money, it is cheaper to build yourself, in my experience. But you need to do some shopping for the parts and you need to buy a bulk reel of cable. And the price benefit will only be seen if you are making a lot of cables. Maybe you don't make them all right now, but if you make a lot of cables over the next five years, it will be worth it.
I am not sure which wire to use, I have a spool but it is not handy and I can't remember what it was I bought. I know there are just a couple balanced cable types you should be looking for. Do some searching and you should find it. Belden is one company to search under. Or maybe someone will post the answer in this thread. I have seen where folks have mentioned what XLR cable to buy on Gearslutz before, so maybe a more thorough search on here would reveal the answer to you.
Now there are certainly some other benefits to building your own cables that have NOTHING to do with saving money....
#1--you'll get to practice soldering if you have not done much of that up to this point. It is a worth while skill IMO for someone who is pursuing a career in the audio world. It can be where you develop your soldering skills to tackle more involved electronics projects that can save you a lot of cash in the future, assist in repairs of other gear or permit you to make stuff you can't buy even if you do have unlimited funds.
which brings us to #2--you can build specialty cables that meet your specific needs that you either can't buy anywhere or will have a hard time finding and even then the specialty cables could be ones you might not be able to afford. Plus the unusual cables that you might need that you CAN find in stores may well be lower quality than you could build yourself, especially after you have honed your soldering chops!
Think of unusual lengths of TRS/ balanced cables for in your rack---you could build them specific to your task. Think of a 150' long mic cable in the odd chance you might need something like that---I needed one for a press conference today to run across a long ballroom. Who knew, right? Yes, yes, yes, you can simply plug two or six XLR cables together to accomplish the same task, but then you have all those potentially wobbly XLR connectors waiting to get stepped on and break the circuit.
So to close, I do indeed advocate building your own with those certain caveats I listed above. At first you will be building a skill set, so think of it as a college expense, similar to text books or the like and then it might be easier to justify. Eventually you will get really good at it and then you'll have awesome cables to use for a variety of tasks.