With your parameters, (Tahoe tow rig, sleep 6, $20K Budget, quality build, first trailer), it's somewhat akin to "Unicorn hunting". :B
Seems most folks buy a trailer, then decide they like something better soon after, or have to upgrade the tow vehicle, lots of wasted time and money. Often times, it's smarter to buy used, try it out, and hit the market again after a few seasons of working things out to your liking. For me, the industry only has a few brands that have decent quality and yes, they are way out of your price range (and mine).
So here's a curve ball that some might disagree with, but hear me out. One of my favorite brands for build quality, doesn't exist anymore, (well, they got bought out by Winnebago...), Sunnybrook RV. Small, independent company, quality reputation, loyal customer following. They built Sunnybrook brands for Eastern markets, and identical trailers under the Mobile Scout brand for Southwest markets.
If you could find one, well maintained, stored under cover, it might be worth buying, and updating interiors, and graphics to suit your tastes. (Repair and upgrade parts from a place like PPLMotorhomes is a good start).
The frame and wall structures were top of the line in their day, Aluminum wall and ceiling studs, electronics and fixtures often well above average. Often a little heavier than the competition. Here's one example in your area, that on first glance and at the price and age, you'd probably overlook, but look closer. Sleeps 6, old model, but look at the exterior condition, appears original graphics still look good. "Grandma's House" interior could use some updating, but at that price, you could afford to do that, and maybe even get a new roof installed, if needed. Solid wood cabinetry, with residential hinges, and construction, porcelain toilet, well insulated, ducted heat/air conditioning, etc.
1998 Mobile ScoutIt looks like it might be a 24FB from this brochure:
Mobile Scout brochureWhen you get down to it, the travel trailer brand is really the frame and shell. The interior fixtures, appliances, are similar across the board. Find a well built frame and shell, and you have a good starting point. If a trailer like this is still in good condition, you might save enough to even buy a dedicated tow rig to pull it or your future trailer. I'd rather have a well built heavier trailer with some age, than a fancy new lightweight, that will shake itself apart after a few gravel road trips.
In newer trailers, with standard industry build quality, Riverside RV seems to do pretty well for the price, and customers that have them seem to like them.
So good luck, and welcome to the forum.