"The most important factor to take into account is whether the firm can deliver your ambitions. For example, do their largest and most prestigious practice areas match your own areas of interest? It's worth ensuring that the firm is investing in the growth of these areas since it is more likely there will be opportunities to qualify in an area you're really interested in. Check how much input you'll have into the departments (seats) that you see. It's no good joining a firm with a key practice area of interest if you won't have a say over whether you experience it.
Also think about the kind of clients and deals they work on; are they one of the top or mid-tier firms who work on high-value international transactions for global companies? What kind of exposure would you have to high level work and clients as a trainee with that firm?
Finally, consider where they're based and where they have other offices. Are there opportunities to work in any of the other offices? International firms will expect you to have a global outlook and be open to working overseas at some point in your career."