That's because Network Solutions tend not to sell direct to the end user, they use resellers. To clarify the ICANN point, the vast majority of top level registrars are ICANN certified but they tend to sell through resellers. So you should be checking who the company registering the domain uses to make sure they are ICANN certified as opposed to the top level.
Domain name is really important and you should choose it carefully. I think the most successful domain names are those which are easy to remember, with no complicated words or signs.
I can suggest the following: 1. Very cheap - www mrsite com - their offers £2.11 p/m , £3.40 p/m or £8.33 p/m (see here) They offer hosting and website templates all in one. 2. Very good service. USA hosted - Hostassured.com - they offer hosting from $7.95p/m etc. If you choose the one for $ 9.95 p/m you can host .co.uk domain "within" .com (that is if you have the names already).
I think you should purchase domain from Godaddy .Its provide you with optimum budget .fulfilment services