I worked in Kiev, Ukraine for 5 years in my career (not anymore). Kiev is a source of outsourcing companies, just as India is. And I was part of it – worked as a developer in outsourcing service companies.
In my opinion, and based on what I’ve seen in the outsourcing business, you need to ask people who have worked with the same company. In general, there are 3 factors that you need to consider: 1- access to talent pool, 2- margin that the company takes, 3- reliability and business expertise of the company (e.g. money transactions and so on which you will need to deal with).
If you don’t know who can give you an advise, just find the company profile pages (e.g. on LinkedIn) and see how many employees they have. The more employees, the more other companies like yours trust them. Also check their customers, maybe you will find companies similar to yours in that list – that should indicate they have dealt with similar situations.
If you have questions, do let me know.