The geographical location of the broker

The first thing I look for is the geographical location of the broker. If I find that they are based in a country where the financial industry is, in my opinion, relatively unregulated and under-developed, I quickly forgo signing up. This is terrible news for honest brokers in those countries, but your job as a trader is to protect your capital. If you loose that, then you cannot trade. The onus is on them to convince you that they will do the right thing by you as an investor.
I started out with an Australian broker. Currently I am using an American one. I have not tried UK-based brokers but the British financial industry is one of the best. Companies that are based in countries such as Japan , Germany and France are probably just as good too, if their website speaks your language.

Notice any license numbers that they may have registered with regulatory bodies that act like government watchdogs who oversee the finance and investments industries. These are organizations that impose strict rules to safeguard your investment. Some of these rules may include the requirement that brokers segregate all customer funds from the operational funds of the business. Your money is required to be put in highly-reputable banks and the funds are only withdrawn from these accounts upon specific withdrawal requests.