Looking at MLS data, it appears that you had a conventional loan, and paid $347,500 (with no concession from the seller). The Seller paid $345,000 just a few years ago (2008) and while most of the upgrades were done before they bought it, they did some further upgrades after they purchased (upgraded lighting, added fencing, etc). You got more than 20K off asking price, and hopefully the bank appraisal was at least equal to the purchase price. Best of luck with your new home, and enjoy all that Portsmouth has to offer :)
Without knowing the local market, if you closed and financed your purchase it would be fair to assume the bank did an appraisal and the home appraised for the contract price. If so, this is an indication of a solid transaction....for now.
On the other hand if you paid cash and didn't have an appraisal done to varify the property's value, it may be helpful to have an appraisal done for peace of mind.