Horizon Transport or others long in the business on whom you can find references are the best bet.
You'll probably receive bids based from one zip code to another. $1.50/mile, loaded, would be a ballpark guess.
Your trailer probably went from factory to dealer behind the same truck.
Insurance requirements are a matter of law, not transport company choice, so the coverage should be similar from one to another. Reputation is what matters most.
There are other threads on this same subject. Search.
1990 35' Silver Streak Sterling
; 9k GVWR.
2004 DODGE Cummins 305/555; 6-manual; 9k GVWR.
Hensley Arrow. 10-cpm solo, 18-cpm towing
Sold: Silver Streak Model 3411