I consider myself an expert on vintage computer collecting. I have nearly 80 vintage computers in my collection. OK, some people have much more than me but my passion for them cannot be disputed.
First thing I suggest is to not give up. eBay has been overrun by scalpers that think they can get $18,000 for a stock Apple IIe. That's no joke...I've seen it listed for that amount.
You have to weed through that crap and look at what they actually SELL for. You will find many of them sell for much less.
You mentioned two very popular computers (Apple II and Atari 400). The good thing about being popular is that they made more of them. So they aren't "rare" by any means. Not yet, anyway.
So, if I could offer some advice, it would be:
1) Pick one or the other at first and stick with it. Once you have a good system running, decide if you want to start on the next one. For example, if you pick Atari, then try and grab a few things for it to make it fun to use. Then move on to Apple.
2) If you choose Apple II, don't go for an original Apple II (they SELL for many thousands of $$$). Also, don't go for an Apple II+ (SELL for $300-$800). Instead, get a stock Apple IIe or maybe even an Apple IIc. If you ONLY want to play games, then an Apple IIc is a good option. It takes little space and they sell for about $100 - $140. A little pricey but you won't need much else. Well, other than a TV/monitor. But a good CRT works well with them. IIc's are great little machines but harder to expand. If you want to do any hardware hacking at all, then get an Apple IIe for around $80-$150 or so. Try and get a bundle that comes with at least one floppy drive. The Apple IIe is one of the most versatile machines ever made and the hardware community for it is still thriving. Also, if you get an IIe, make sure it has the SSC (Super Serial Card), disk controller and 80 column card. 90% of IIe's sold have those cards inside. I would be surprised if they were missing. Even if they are, they are cheap to buy. The IIc has them built in (virtually). But you will need them for the IIe. Again, they were VERY common and most of the time, they are still in the IIe when sold. After you get an Apple IIe or IIc, either buy a null modem cable or make your own so that you can use ADT Pro to transfer files over. Or, better yet, get the FloppyEmu from BMOW (Google it). It's about $100 or so but allows you to transfer files from SD card to your IIe/IIc.
Now, there's also the Apple IIgs which is a great machine. And, the eBay scalpers haven't latched on to it as much. But the IIgs might not get you that "nostalgic" feeling you're looking for. Some people claim that the IIgs feels more like a Mac than an IIe and I would agree with that. While it can boot to A2 mode, the detachable keyboard still makes it feel like a Mac. That's not a bad thing. It's just different. Another issue with the IIgs is that you really need to use the Apple monitor that came with it. Which is heavy and adds to the cost. You can use a CRT but it doesn't always look great. So the IIgs is another league, IMHO. Great machine. But different.
3) If you choose an Atari, I would go with the 800 XL. It was Atari's most popular 8-bit computer and they can be purchased for well under $100 if you keep looking. A classic 800 (non-XL) is also great but a little more pricey at around $100-$120 depending on options. The 400 can get a little expensive for some weird reason. The 400 is a great little machine but not recommended for typing. The 800 XL is your best option. Once you get that, look into the SD card or multi-cart options. There are plenty. In fact, the Atari route might be a little cheaper in the long run because they are physically smaller (shipping is less) and they aren't as popular in the "retro collecting community". People are snagging up Apple's at the moment so demand is up for them.
The Atari 8-bit line of computers was really the underdog in the 8-bit world. It had some popularity but nothing like the Apple IIe or Commodore 64.
Now, on your TI....you're right. You'll never get that nostalgic feeling from it if you never used it. But that doesn't mean it can't be fun. It was my very first computer so I have strong nostalgic feeling for it. The great thing about the TI is that it is EXTREMELY active these days! Seriously. It's more active in 2017/2018 than it ever was in the 80's. There are new games and hardware coming out for it all the time.
If you really want to get some miles out of the TI, there are a few things you can do that really makes it (more) fun. First would be get the 32K side-car expansion. All of the new stuff assumes 32K. I forget the exact name of that card but it's pretty cheap to get (even open source if you want to build it). Just go to the Atariage forums and look for TI.
Second would be the SD cart for it. There are a few options for that now. Which allows you to load software from an SD card. It's also pretty cheap.
Finally, if you have a little money to spare, try and get the F18A replacement chip for it. The F18A is a 100% cycle accurate replacement for the TI's video chip (the TMS9918). This chips allows you to connect to a VGA monitor and it looks AMAZING. Plus, it adds some additional features like more sprites, blitter and smooth scrolling. There are new games coming out that use the new features. This option is a little pricey at around $90. And, you will have to do a little surgery to your TI. But it's not hard. No soldering involved (TI socketed the TMS9918). But you will have to run a cable out the back. There are also people that will do it for you.
Now, the CoCo2. I own several CoCo computers (version 2 and 3). I have to admit, I'm not very active with them. I never had them as a kid (my cousin did). Also, the community seems a little less active with them. Not sure why. It's a platform I'd like to get into one day. But I can't offer much advice on it now.
After all of this, if you still want to get into collecting, my next recommendation would be the mighty Commodore 64. By all means, go for Atari and/or Apple II first. For that nostalgia. Then, if you're interested, try your hands at the C64. Nothing beats it for games.
Sorry for the long winded response. But like I said, I'm very passionate about these machines. Let me know if you need any more advice.
Let us know what you decide!