I know Mateo posted pretty much this already, I was already far into writing this so I'm posting anyways.
I would suggest using the TI 84 Plus CE (I'll refer to it as the CE), though if you need a cheaper calculator The TI 84 Plus is pretty good too. Do NOT get the TI 84 Plus C Silver Edition (I'll refer to it as the CSE). The CSE uses the same processor that the TI 84 Plus uses (the Z80) but with a more powerful screen. Since the calculator has to spend more processing power on the screen, it makes the calculator terribly slow.
The CE on the other hand has a slightly newer processor (the eZ80) which allows it to handle the new screen much more efficiently. The CE also has a wide community experienced in BASIC (the built in language), eZ80 Assembly,
ICE (A new language made specifically for the CE), and C.
To elaborate on whether a monochrome game is compatible with the CE:
In short, yes and no. Yes there are several programs that will completely work, but the majority of them will either technically work but not really (I'll explain), or won't work at all.
>A few BASIC programs use the home screen to display their content, these programs may still work on the CE.
>Some BASIC programs use the graph screen to display their content. However, the resolution of the calculators screens have changed dis proportionally (from 96x64 to 320x240) so the scaling of these programs will be incorrect (They will appear highly scrunched and impossible to tell what is going on). So even though it may continue running, you won't have any idea what is going on in the program. Also, if the program uses pictures, you wont be able to send the monochrome pictures to your calculator since the CE wasn't designed to read monochrome pictures.
>I'm not ASM programmer, someone experienced in ASM could explain this part better than I can, but this is what I think: You won't be able to run any ASM programs for two main reasons.
1. The processor changed from a z80 processor to the faster ez80 processor. Doesn't look like much of an upgrade does it? Actually, the code for z80 and ez80 are quite similar, however porting programs from the monochrome calculators to the color calculators still isn't quick nor easy.
2. The screen again, the monochrome 84 ASM programs were designed to run on a much smaller screen and sadly can't just 'rescale' themselves.
Note: There is a TI 84 Plus ASM emulator being developed which will allow you to run TI 84 Plus ASM games on the CE, but it's not released yet.
In summary:
>BASIC programs that use only the home screen may work.
>BASIC programs that use the graph screen wont display correctly.
>ASM programs wont work.