What size wire? Whatever size you happen to have handy. Size isn't going to make any significant difference if it's strong enough to hold it's self up.
If there's any particular band that appeals to you, I'd make the antenna of a length that would favor that band. If you don't have any particular band of interest, then in general, the longest antenna you can conveniently manage should do fine.
The 'problem' with running antennas 'back' on them selves is that some portion of a signal can be 'neutralized', 'wasted', sort of. That deals with frequency and wave lengths, a particular 'length' being better than another in that relationship.
If you continue the run of wire back to the radio, the whole thing becomes part of the antenna. That can be either good or bad, just depends on what that part of the antenna is run near. The one thing that people seldom remember about longwire/random wire antennas is that theydo require the 'other half' of the antenna, a good ground system. Lots of variations in that, but all antennas need that 'other half' to work well. That other half can be in the form of a 'ground', or just another length of wire (feed the thing in the middle). You have gobs of alternatives. Got metal window screens? Just for grins, hook a wire from one to the antenna jack on that radio, you might be surprised. And antenna is just an electrical conductor of signals. If it's electrically conductive, it can be an antenna, or part of one.
Have fun.
- 'Doc