I am a calculator collector and have many of them.
Criteria: Polynomial solver, not graphing (or doesn't look like a graphing calculator; narrow screen)
bold if still in the sales channel
Hewlett Packard: HP-28S, HP-42S, HP-34C, HP-27S, HP-35S, HP-15C LE
Casio: fx-880P, fx-5800p
TI: TI-68
The most interesting ones of these are as indicated by helius not available on retail anymore and even as second hand devices they reach relatively high prices. This is especially notable for the FX-850P/FX-880P (I have three of them), not to mention the HP42 series, which sell at ridiculous prices! The legendary HP 11C, 12C, 15C and 16C are also great INVESTMENT WISE, as they reach record prices on eBay (I was lucky to get hold of a well preserved HP 11C for little money).
The reason for these prices is due to the easy and powerfull operation with great user interface. In case of the CASIO FX-850/880P, it's the BASIC programming language and the fact that they can be hooked up to a PC using some wires for RS232 communication.
If graph calculators like the HP 50g (end of life, mayby you get it on a sale), HP Prime or TI Nspire are not allowed, then I would really go for the calculator which is RECOMMENDED BY THE TEACHER!
Modern math classes require students to follow exercises on their calculators and if you have a "different" one, which is unfamiliar to the teacher, you might get stuck with some exercises.
Better to get the recommended one, which will probably inexpensive and if you desire, get yourself a propper calculator or just install an emulator! I use the HP 48GX on my Samsung Galaxy Note4 and it feels like the real thing I used to have while at University. It even runs the programs I made back then.
Beware that modern calculators like the HP Prime and TI Nspire are made for classroom featuring problem-sheets and stuff like that. The HP Prime is still an excellent engineering tool, I do dislike the TI Nspire a bit in this regard. Both are CROWDED with functions and you either spend a LOT of time figuring them out, or you will have a hard time doing whatever advanced calculation!
Regards,
Vitor