Cool project! I suppose that your choice of processor (and reason for needing external memory) will depend on how you define "simple graphing capabilities" and "limited programming ability".
Stop and consider that the TI-83 calculator has a 6 MHz processor, uses 8KB of RAM for system functions (24KB is free for user programs), and has 512KB of Flash with an external 2MB Flash chip on the special "Silver" editions. It runs a proprietary OS, and has support for more mathematical functions than I've ever heard of or used, as well as programming in 4 languages. Your ATMega1284 has 16KB of RAM and 128KB of Flash. Do you think you're going to generate enough code to fill those 128KB, given that TI only used about three times that much? I doubt it.
If you just want to use a character LCD and a LED array for graphing with basic math functions (Buttons 0-9, variables x and y, +-*/%=, and some kind of storage), then an ATMega or Arduino is more than adequate for your needs.
If, on the other hand, you want to run a color TFT with embedded Linux, scripting/programming in bash, lua, or whatever programming language you choose, graph with gnuplot, and enter everything on a mini querty keyboard/numpad, then you should look at more powerful chip. Definitely go for 32-bit if you want to deal with big numbers, and if you want to address lots of memory. Most of these chips (I recommend ARM) come in QFP packages - But don't be afraid! You don't need expensive machines to solder a [LT]QFP or PLCC device - Just a steady hand, a fine tip, and decent technique will be adequate. Oh, and a well-made board with soldermask. However, many dev boards will be well suited to this project.
You can buy these chips in singles for $2 to $15, depending on the options you want. Also, many manufacturers will send samples if you just ask, in hopes that you'll buy thousands once everyone is taking the ACT and SAT on an EARLZ-9000 calculator!