You don't mention if this is a place to host your own servers or just your apps on their servers.
If it's for your own servers ask about;
- Would you be in dedicated or shared rack/s - this may be important to you, do you trust other companies working alongside your servers? have you the skills to harden your servers for this situation?
- Do they provide the racks? if not what racks will they be happy with (i.e. all three dimensions, weight)? what power (in watts) do they provide to the server or rack, is that max or average, how do they deal with power-bursts as often seen at server boot up? what power outputs do they provide (regular sockets for your country, 32/16amp, 3-phase etc.), what about cooling, how many BTUs/hour do they commit to scrubbing, how do their coolers work (hot/cold row? neutral incoming/negative outgoing? etc).
- How do they deal with security, can they hold keys for you, how do they deal with local operations - do they have 'remote hands' to help you with stuff, how do you get your own people or suppliers access to your kit? Do they cover your servers with video cameras, if so how long do they hold onto the video? Do they offer an access-list so you can restrict who goes near your kit? Can you get a live feed from their cameras?
- how do they deal with external cables/fibres - who puts them in, how much do they charge, do they let you do it yourself.
- Would you be allocated any on-site storage for cables, tools etc.? if so is this close to your servers?
- Do their ops team have tools you could use/rent/buy on-site if needed, things like trolleys for moving hardware are a godsend when you need them.
- What about parking and deliveries, how does that work, how long do they hold onto your deliveries, are they secure, are they 24/7 or just 9-5, do they email you when something's come in for you? How do they deal with large and/or heavy loads, what about rubbish removal, do they do that?
- What do they do for UPS, do they provide that to the room/rack/server or do you have to provide it? if so how do they deal with UPS maintenance? what's their power-outage record? Do they have diverse power inputs to their buildings?
- Obviously commercial concerns, costs for the basic service, what are the additions and what are the rates, how do they deal with unexpected work - do you have to produce a PO before they'll work or will they work 'at risk' first?
Those are the basics I'd be asking, someone else would have a similar list for app hosting, I'm less of a user of that type of service myself. Hope this is of some help.