From my experience with MongoDB there are a few things to think about.
MongoDB is a document based database, using the standard driver from 10gen you can serialize POCO classes directly or store you data as an untyped document.
This does bring a great deal of flexibility as you can store a complete record about a user store and retrieve it without having to normalise the data as you would with SQL Server.
That being said the Full text capabilities of MongoDB are very limited compared to that of a SQL Server, see the link below for details of how to do a basic full text search in Mongo.
http://www.mongodb.org/display/DOCS/Full+Text+Search+in+Mongo
MongoDB really come into its own when retrieving data as it is attempts to store the DB in memory, this makes getting data from it pretty quick.
10gen are also implementing Linq support directly into the driver which makes querying Mongo just that bit easier when getting started. Also you could use FluentMongo (https://github.com/craiggwilson/fluent-mongo) which sits on top of the 10gen driver and is slightly more advanced in terms of its Linq support.
My experience with MongoDB has been very positive and intend to use it in the future for other client projects.
With hosting I would imagine you would want at least console access so that you can start the DB service and manage any backups. Failing that you could try something like https://mongohq.com/home which seems to provide online hosting of mongo db.
I hope some of this is helpful