I run a design agency and have helped countless startups designing their websites and products. Here is my advice whether you get someone from India, China or locally to do it.
1. Figure out if design is part of your overall strategy or whether you simply need a presence.
With this I mean figure out how important design is to whatever you are launching. Many startups put too much time, money and effort into making their website perfect only to find out 6 months later they need to pivot or change their communication efforts. There are generally 3 situations where it's going to be important to spend time and money on a good design agency or designer.
If you have developed a technology that is complex in nature and needs to be productized and communicated to lay people.
If your design is going to be a differentiator to the rest of the market. I.e. in markets where there are many competitors but few of them (or most of them) have spent time on making their design really stand out. For an example of such a market see the time-registration market which is huge and diverse. You do though need to
If you have a clear vision and know you won't be changing that vision anytime soon. It's rare but it does happen. But just as with 2. you need to be clear in your mind yourself about how you want to stand out. I.e. create principles. You might want to read http://000fff.org/beyond-aesthetics-design-tips-for-startups/ for what I mean with that.
2. Always get a portfolio and have them explain what parts they did.
You will be surprised how many times designers show some work they have been involved in but not necessarily done everything off themselves. It's fair enough that they do that, but you should just make sure that you figure out whether you are appreciating the right designer.
3. Hire them in phases
Instead of getting one price on the entire project, hire them one phase at a time (UX, Visual Design, Front-end programming, development). This will benefit both of you. You will figure out if are a good match without having betted your entire budget in one basket and they won't be stuck with this stupid client they hate if it would come to that. It will also give them something to work for (next phase) which means they will often put more effort into the first phase (again a benefit to both of you).
4. Pay them 25% upfront
This might sound weird but since you are a startup they are running a big risk taking the job. I know many stories (and have experienced them myself once in a while) companies getting a lot of work done without having the money. So to get that insecurity out of the way do this. Many agencies will ask for it anyway (some even more) because they have burned their fingers too many times. There is a huge advantage to doing this by paying 25% upfront you are putting the pressure on them to work those hours as quickly as possible it also removes any argument internally in the agency about whether they should put their best people on you or prioritize bigger clients.
Work on getting an internal team Whether you have hired an agency or a team of freelancers work on getting your own people. Outsourcing means paying for their time this is beneficial if you are trying to get started and don't have the capital or is in a position to hire your own people. But once the main project is over you will be better off having someone in your own stable rather than having to pay for an agencies time. The second you start having ad hoc assignments, changes which where not part of the agreement etc. the agencies will down prioritize you since you aren't bringing in the big bugs anymore and you will loose most advantages with regards to their cost. As an alternative this might be where you outsource to China or India as they majority of conceptual work have now been done and your tasks are less complex.
If you can afford it get a copywriter Unless you are a savvy writer yourself you will benefit greatly from getting a good copywriter to help you communicate your product as clearly as possible. Good copywriting is half of the design experience, this is why advertising agencies often have teams with one art director and one copywriter on each.
Hope this helps.