One of the things you need to consider is not just the nature of the work you're looking to outsource, but also the volume. There will be upfront costs both for you and a selected partner, so you have to be confident that you will have enough future revenue to justify the investment. You may want to start with the type of work that is currently your highest volume, so you can use it to sort out the logistics of doing work with your partner, then expand to other work types once you have the basic workflow sorted out.
Outsourcing to India, or anywhere, can be really great and at times really frustrating too.
Following are the things that you need to look out for:
1. History of the company / individual
2. Rate the company is offering (based on your budget)
3. Experience of the outsourced vendor to accomplish the specific desired work, etc.
It is always best to follow an organized process. Following is a simple sample process you could start with .....
1. Initial discussion
2. Project requirement analysis
3. Submission of Time and Cost estimates
4. Negotiations and iterations (estimations and team members)
5. Finalization and contract
6. Introduction of Team
During the development process get involved with regular communication (phone, email, written), team meetings (internat as well as joint via video conference), and a beta testing phase. Don't just jump right into it. Contact, communicate, test, verify, and make sure your expectations are clear and met. I'd also suggest to include agreed upon penalities in any agreement in the unfortunate case of unmet deliverables or performance expectations.