There are major differences between the IIc and the IIc+. And there are 2 versions of the IIc itself.
The biggest is the PSU. In the IIc+, the Power supply is internal to the IIc+ and plugs into the wall directly. The IIc has a simple step down transformer to bring 120VAC down to 12V DC, and that goes into a power regulator board inside the IIc. This, strangely enough, allows the IIc to be powered by a 12V battery if you can rig up power jack for it.
The first (older) version of the IIc has few options to upgrade. you got 128K, 2 serial ports, floppy port, video, etc. and that's it. If you more RAM, lets say, you have to get a specific board and hard wire it in. The second (newer) IIc has a RAM Expansion port, as does the IIc+. This allows you to plug in a RAM Board and even a Z80 Card into the IIc; they are made by Applied Engineering and other companies and lets you have up to a Meg of RAM into the IIc.
The serial ports on the IIc+ uses the standard Din 8 ports used on the Macs. The ports on the IIc uses Audio style Din 8 pin Jacks.
The Disk Drive is different, as the IIc uses the "standard" 5.25 inch drive and the IIc+ uses the 3.5 in drive. This is the same 3.5 inch drive used in the IIgs. The IIc+ can use a 5.25 drive you plug in to the back, like the IIgs. And here is where is gets tricky. The older first version of the IIc only uses the 5.25 inch drives; the second newer version of the IIc can use both 5.25 inch and 3.5 inch drives.This is because the IWM/SWIM used inside the machine.
The first (older) version of the IIc does not have what is known as "Mouse Text" in ROM. Mouse text allow ProDOS to have those psuedo windows/folders open on the screen. Thus for ProDOS to have that, it must load them into RAM. This is no big deal in my opinion. the second (newer) version of the IIc and the IIc+ have Mouse Text in ROM. Since ProDOS does not have to load Mouse Text into RAM, so it does speed some things up.
To get 3.5in drives and Mouse Text into an older IIc requires an upgrade of the ROMS and the IWM Chip. Apple used too have this kit but it has been years since I seen on. But that may not be necessary. The Mouse is also different, the IIc uses the older Aple IIe/Mac 128 Mouse, and the IIc+ uses a IIgs/Mac ADB Mouse.
Before I forget, I believe the IIc+ has a faster CPU that you can set into Turbo Mode. I could be mistaken on this but I remember something like this in the IIc+.
For a BASIC Apple II system, the IIc or IIc+ would be the best option.
Another harder to find option is the Laser 128. vTech made an Apple IIc Clone/compatible unit. It's bigger in size and has a built in keypad. But it also has an Apple Slot on the side of the machine to add a card onto it. When I had it, I used a EPROM programmer on it to burn ROMs with it. thing is, the card hang outside ot the unit on the side. It also has the a turbo switch to run the CPU at 1MHZ or 4MHz - which I believe is in the IIc+.
Amassed a collection of various Macs and PCs that friends are calling my place a Mac museum: 512Ke, Plus, SE/30, IIcx, IIci, Q950, Q800, Q8100, 7100, Biege G3, PB 5300ce,190, 190c, 150, 180, (4) Duo 210, Duo 230, (2) 250, 280, 280c, 2300c, (3) G3 Wallstreet, iBook G3 (Orange), (3) iBook G3 (White), (3) iBook G4, PB G4 (all 12in)