NetworkSolutions is a well-known registrar. We've used it for years, but its sketchy in the way they attempt to trick you into paying for services you don't need (auto-checked non-essential services and the TINY little button to say no thanks), their support is horrible (dont even bother calling unless you're the adminstrative contact on record; technical contacts need not apply), and their zone file management is buggy (ever try to add a CNAME www record? wow, is that painful!).
If you're registering a new domain, I recommend going with someone other than networksolutions or godaddy (who is similar to NetSol in so many ways....). For new domains, I favor namecheap or hover. For existing domains that are already on networksolutions and for whatever reason, its not feasible to transfer it away, then I recommend Amazon Web Services (AWS) Route 53 to be the nameserver / zone file manager. Compared to the difficulties of modifying the domain records on networksolutions, AWS Route 53 is a akin to a glorious cartoon-style romp through the meadow while the sun smiles down on you. And the price for using AWS Route 53 to host the zone files? 50 cents / month. True, its an extra cost to do what NetworkSolutions technically provides, but your stress levels will thank you. Or better yet, completely transfer away from NetworkSolutions. Its awful.