Right off the back I would want a host who has very reliable support.
Must has 24/7 support in house of course. typically cpanel/whm is always a must.
lately ive been really falling for ssd drives so that can also be another thing id look for in a host.
Price wouldn't be a issue at all, I've come to realise that with hosting or any services these days you get what you pay for and of course .
Who has the coffee pot?