What are the best Forex trading platforms/brokers?

The best is a vague term. What is good for one person might be completely useless for another and vice versa.

The most popular platform for retail Forex trading is MetaTrader 4 (MT4). This platform is used by the majority of brokers around the world.

The advantages of MT4 are numerous;
1) It has most common tools for technical analysis, which are very easy to use, adjust and modify.
2) Building custom indicators is pretty simple.
3) MT4 allows creating of automatic and semi-automatic trading advisors also known as trading robots. Based on the user trading system’s parameters, these advisors can either prompt the user to trade manually or just trade by themselves automatically.
4) There is also a simple-to-use built-in strategy tester, which allows testing your strategies and trading robots on historic data.

As for the broker, the one of the biggest and reputable is Oanda. Depending on where you are, you might want to use a local broker. There are other considerations for choosing a broker such as a minimum account size, allowable lot sizes, margin requirements, ease of depositing and withdrawing funds and such. Prior to committing any money, I would recommend searching the Internet on the broker you choose and especially on the comments that people have about that broker.