You can use the plug off of an RCA cable, just solder the end of the antenna to center wire coming off the plug. You could use RG59 as the feedline if you wanted to reduce interference, just solder the center wire of the RG59 to the center wire off the RCA plug.
The L under the eaves sounds like a good idea. For a while I had an antenna that was about 40-50 ft running under the eave line on the underside of the edge of the roof. I got good results.
An L would be o.k.. Shortwave antennas don't get really very directional unless you have a longer antenna, maybe longer than 100 feet they'll get directional (a shorter dipole cut for a specific band would be directional, though, but for most single wire Shortwave antennas you just run as much wire as you can). Even so, having an L could help, especially on the higher SW frequencies.
For general SW listening, I don't think there is a "best" length. But usually, longer is better.
I don't use a ground. And when I did, I didn't hear any difference. But there are others who swear by using them.
A more important thing is to ground the antenna if there is T-storm activity or during winter when the air is dry and static-y. Static electricity, and T-storms aren't good for radios. So find a way to ground it when unused, if you can.
Hope this helps.