Trailer? (its a dirty word)

[BR3W CITY]

So I'm an all-out "Drive it there you p*ssy" type of guy....but even I can appreciate the NEED to trailer your junk around from time to time. Its about time I purchase a trailer for my rig, but could really use some advice. I'd like something for the occasional track weekend, and mainly because I'm moving and anticipate the need to be able to relocate my truck and gear several times in the next few years.

Absolute base requirements: I'll be towing it mainly with my 05 Yukon (5.3, 4wd), and it needs to be a trailer large enough to take my '66 and some spare parts. Budget is flexible, but under $6-8k for something with options or $3-5k for something more minimal.

MUST tow behind my Yukon (no 5th wheels or gooseneck hitches)
MUST carry my '66 and a few spares
MUST have onboard brakes
MUST be well built and safe.
PREFER extra room for a toolbox or workspace (if enclosed)
PREFER room for spares/tire rack/ramps (if open)
PREFER side access to contents (if enclosed)
PREFER lightweight to make it easier to tow on a normal truck.

Sooo...what do you guys recommend? I'd really like an enclosed trailer for security when parked, and an allweather work space at the track. I understand weight will increase, as will cost. I'd love to hear from all your experiences with trailering.

Oh, and for the open trailer guys, do you car cover/tarp etc to protect your ride? Tips?

Thanks!