I can't offer opinion on L.E.D. vs conventional, but I'll got a couple of general tips for ya.
1) - The easiest location to find for the group of wires you'll need to tap into are under the seat. You'll see the wires for tail, stop, left/right turn & ground. You'll need a 5-post connector (one for each of the fore mentioned circuits). The colors of the connector wires is not important, so long as you match on both ends. For example: turn signal wires (left is orange, right is blue). If the connector has purple and pink, you just need to figure which one on the trailer is left and which is right to connect to the proper wire on the bike. I've always tried to match any like wires when possible...If the connector has a green wire, that is automatically "ground", just like the bike, etc...
2) - My preference has always been for "most lights possible", so I would put two separate lights on for tail/brake (red) and turn signals (amber). It all depends on the trailer mounting space (and your budget, of course).
3) - Solder and heat shrink are your friends. I took ONE soldering class when I was in the 8th Grade (1979), so when I went to do the infamous "3-yellow wires" on my 1100, I relied on a you tube video to refresh my memory on soldering...If I can (successfully) get that job done, anyone can.
I just recently added a trailer hitch to my 83 1100...But I haven't yet put on the wiring connector (but that's mainly because I don't have a trailer - LOL). When I do add the connector, and I know that I will, I'll ask that someone take pictures as I go along. I apologize if I don't get it done in time to be helpful to your project, but it can still be shared for others...Safe riding, my friend!