Most outsourcing agreements are governed by service level agreements (SLA). I would investigate what those metrics are likely to be and what your company's ability is to achieved them. If you Google RFP's in your industry you may be able to find examples of SLA's.
Our company has played roulette with outsourcing and lost EVERY TIME when it came to searching on sites like ODesk. The problem is (and although they try to keep it at bay) there is no standard of quality. Think about it - If I am a web designer and I think I do good work, and Joe is a web designer and thinks he does good work, who actually does good work? It is normally for the client to decide who to work with, but the client doesn't have the education to know what good web design really is. This depends a lot on trends, web development needs, etc. What I recommend is starting with your closest group of professional friends and see if they have anyone they would recommend for outsourcing. We have had our best luck through recommendations. We have a project manager that was recommended to us that is located in the Philippines, speaks perfect English, works VERY hard, and is attentive to the smallest details. The chances of finding someone like this on an outsourced service website is about 1 in 100. Hope that helps.
location, location, location. Really. Do you want to outsource to people across the globe and have conference calles at 2 in the morning? Can you really manage people from thousands of miles away and who in your org will manage these people? Is your IP protected (in places like China or India)?
Check the name of the agency or person you are considering to hire for outsource work. Check the Track record, how long, how many clients, how many good recommendations, specific skills, etc.
Do a check up exam on the prospect. Investigate how the prospect operates, how trustworthy, how skilled, how dedicated, how motivated, etc.
Do an interview. Online or face to face if possible (Skype, VOiP, phone, etc)
Ask for recommendations from your business buddies. Know what you want so you can get the perfect match for an outsource. Good luck.