Is you whole budget $4k? or is that what you've set aside for the tax, title etc? If that's the whole budget you'll need to look for a trailer under $3k before tax/title etc which will limit you to an older pop up style. That cheap of a trailer is going to be older and will likely need work done to it (tires etc) Definitely not what you want if you plan on full timing later on.
If you can swing the cost I would also suggest a hybrid. You won't find much in bunkhouses with a separate queen bed under 26'. That size and weight will push the max limits of an older Sequoia. A 21' hybrid will be much lighter and shorter to tow but will still have the space of a 28' trailer once the ends open up.
Another bonus of a hybrid is they seem to depreciate faster than other trailers so you can get them cheap. Some downsides? Added set up/ take down time, tent ends prone to leak, not good in colder climates, less secure.