There are some things here that aren't correct for New England.
In Rhode Island (as in the rest of New England) title companies are not commonly used like they are out west. Your best and cheapest way to go is to hire your mortgage company's (or bank's or credit union's) attorney to also represent you. I've done this several times and it's a couple hundred dollars. Since the attorney will search the title for the bank, they do literally no extra work representing you. They can also handle closing. I've had this done several times.
Do NOT, NOT, NOT rely on some internet value on the house. Case in point: My wife's aunt went into a nursing home and as POA, she got the sale of the house going. It was built in 1890 and was in need of a ton of repair. I joked that the knob and tube wiring was holding the house together and a coating of asbestos and lead paint dressed it up. But seriously, it had all that. Zillow estimated the house to be worth $295k. It sold for the top bid of $135k, which impressed me as I had predicted that it would never go over $80k. Thinking it is worth $450 and a bargain at $400 isn't doing your due diligence. You want an appraiser to go over it and give you a realistic number. The example I used above was on Vernon Hill in Worcester, so less than 100 miles from anywhere in Rhode Island and with the same accent, dropping "R"s from words (horse = haas) and using them in words that don't have "R"s (idear). :D