Assuming you already have an adequate hauler, properly setup with good brake controller, here's a few thoughts...
How much work do you want to do to the trailer in the beginning? Are you willing to buy a used trailer for cheap and re-deck it, new lights, new jack, new paint, etc., etc. and whatever else it takes to turn it into a good runner again? I've bought and sold many used trailers in rough shape and re-built them to turn a profit. Kept a couple, but overall, it's kinda fun. If you're willing to look for the "right" deal, you can get them pretty cheap. to the other extreme, you can spend a small fortune on a used trailer in decent condition for the wrong deal and not have to do a thing to it. Be smart with your purchase and don't be afraid of the "little" things if need be. Sometimes the deals are too good to pass up.
I'd personally not go less than 10K-you run out of weight real quick with a loaded LJ, gear, supplies, etc. Lots of carhaulers are 7000lbs. (twin 3500lbs. axles) and this is NOT enough for a week long camping trip with a loaded Rubi. I always go larger than I think I need on the trailers axles-my 18 runs twin 7,000 lbs. axles-and I've used every bit of them.
16' is kinda short-I like 18' but 16 will work.
Aluminum-nice, but $$$$ and I doubt you'll find many used that you'll want to rebuild for cheap-likely get top dollar even for used ones and there better not be anything wrong with it used either unless the price is a steal...
Steel trailers-great depending on how they're built. I prefer wood decks for many reasons. I think all my trailers are steel with wood decks with the exception of my current off-road trailer I'm building and a few of our stock trailers, which are aluminum and/or steel. One or two is a mix of both. I like steel.
Brakes-get them on both axles. Some states are OK with just one axle, but you'll be much happier and able to run in my state should you choose with brakes on both axles...
Sides- I wouldn't worry about them. If you want them later, build them for cheap to use the trailer for utility work. Definitely would NOT make or break a deal on a good trailer without sides...
I'm personally not a fan of the beaver tail, but that's just me. Ramps are fine. Lots of folks love them. Beavers still have ramps, just lessen the angle a bit.
Look it over carefully, ensure frame is sound, not tweaked or bent, or other damage. Don't worry about the jack too much-I go through a LOT of jacks on my trailers. They're cheap and an easily replaceable part. Wiring, lights, etc., are all easily replaceable and relatively cheap. Tires-just like the Jeep, they're a maintenance item. It's a bonus if you get a deal on a trailer with good tires, otherwise plan to replace. You'd be surprised how many Brand New trailers are sold with tires that are NOT rated for the trailer they are on... Paint is cheap/easy. Don't forget markers and reflectors/reflective tape. Check your local state laws for rulings on that. Be sure to have the 7 pin RV style wiring plug whether you buy with or re-wire it. You can always go DOWN in wire/plug size but you can never go back up. Meaning, you'll want brakes on both axles, marker lights, stop lights, possibly backups, possibly accessory power, etc., etc. A 4 flat won't allow any of those items... Believe it or not but I have seen a few cobbled together 18's with 4 flat wiring. :roll:
Most of all, Have Fun!!!
Best of Luck,
Mike