You'll find as many opinions on web hosts as you will people on the internet. ;)
osTicket doesn't require much in the way of server resources. It should run fine from any shared hosting environment. For the most flexibility and future compatibility, just pick a host that allows you to set up cron jobs (currently used for optional POP3/IMAP e-mail polling) and supports PHP5. Fortunately, both of these are very common/typically standard things.
Personally, I've used and love the service and reliability of both Site5.com and ASmallOrange.com