If you want to build from scratch go for it. Another approach would be buy a cheap one all assembled - for $100 or so - used Squier Bullet Tele, Indio, etc. See what you like and don't like and replace/experiment as you get funds. Then you start with something that works. Good luck! Report back on your progress.
As a builder of many partscasters over many years, I also agree that this is the best way to dip your toes into the guitar-building ocean. There are a lot of little things and variables you don't think about until you actually have to deal with all of them putting a guitar together. I recommend going with Squier if you can because for the most part generic Fender-style replacement parts will
probably fit. It is still important to know whether and how dimensions (bridge width; tuner hole diameter, etc.) on the parts on your guitar vary from the vintage Fender dimensions that seem to be the norm for aftermarket parts, but even if they do, there are often parts available to fit Squiers that may not be avialable for some less prominent and Fender-connected brand. Taking a Squier and replacing different parts over time will give you experience working with the various parts of the instrument, and perhaps some insight into the characteristics you prefer in different components. You may well end up with a really nice instrument, but even if you don't, unless you've done a lot of drilling or something you can probably swap the stock parts back and sell the Squier for roughly what you paid for it.
The difference in sound and/or playability is tiny. IOW, partscasting can easily be a deep rabbit hole.
This is also true. While I have built some great guitars and had a great time and learned a lot doing it, if the house burned down I probably wouldn't bother building more Strats or Teles versus just buying Strats or Teles and maybe making a couple tweaks.
In building a DIY Tele, I had a lot of problems with aftermarket parts not fitting.
I've had this too, and for that reason I don't recommend building a ground-up partscaster for your first build if you're on a budget. I've built guitars with cheap components and some of them have turned out really nicely but they all took more work to get things together cleanly, and I've seen multiple cheap instruments and components where the mounting holes for major components (neck, bridge) are not drilled squarely. If you want to build a guitar completely from parts go with either actual Fender parts or Warmoth. After buildling guitars with a couple cheap bodies, and having a friend get one that was drilled wrong, I've sworn off of them for any serious purpose, and would expect to have problems if I did order one.
Finally, there's assembling parts, and then there's turning those assembled parts into a good guitar. Things like nutwork, fretwork, wiring, and setup are hugely important and make a big difference whether you are dealing with a partscaster you made or a pre-made guitar you bought. To build a
good partscaster those are skills you need, and you can practice them on any cheap guitar. But bolting together a gutiar and then not knowing how to dial it in to play really great, with smooth level frets, nut slots cut correctly, and a good setup, seems almost like a waste of time.
P.S. If you go with a Tele, note that new Tele bridges and old Tele bridges, while they may both fit, have the saddles in different places, and a new bridge placed in the old bridge location will not intonate, and vice versa. Lesson learned the hard way. Read a lot and don't repeat other people's mistakes, including mine.