I'd put the hard drive inside the LCIII+ since you're more likely to run programs that require system additions such as QuickTime on it. Additionally, if you don't have the System 7.1 disks that go with it, you'll need System 7.5.3 from Apple's site (they don't have 7.1, just 7.0.1, which won't run on an LCIII+). 7.5.3 is a massive install but 7.0.1 can be snugly fit onto a floppy such as the Disk Tools diskette.
To use your Classic II, do the following:
1. Make sure your Classic II has the full 10MB RAM installed. If it doesn't, find some extra RAM (you can always ask on our trading post).
2. Find the excellent shareware program RamDisk+. I'd go with 3.23 or higher for your version number.
3. Install the program on the Disk Tools floppy or other startup floppy. Remove the Apple HD SC Setup program since you have no hard drive to set up. This will also give you some extra room if you want to install some of Apple's control panels (General Controls and Brightness are recommended for a Classic II), fonts (if you will be word processing at all, make sure you have a serif font such as New York), printer drivers, or third-party utilities. Disk FIrst Aid can get tossed too if you need some room, although it does come in handy if you have a bad floppy at any time.
4. Set up a RAM disk that, at startup, copies your system files to the RAM disk.
5. The system will be running from the RAM disk. You now have the internal floppy drive to use for programs and can pick up even more power if you spring for an external floppy drive (usually less than $20 on eBay).
The RamDisk trick works very well, as it eliminates disk swapping. There are probably other programs that accomplish this, but RamDIsk+ is one I know will work like this. I'm not sure if the guy who wrote it is still around--anyone try registering this program lately? (I'd send a check anyways, since it's your ethical and legal obligation to pay for shareware you use--let me know if you get any response back when you send it).