As you would expect, a full service brokerage firm provides the most comprehensive package of services. If you want investment advice and recommendations, you'll want to pick one of these. They have analysts to analyze, researchers to research, and brokers to buy and sell. If you don't feel you need or want any of that, you can use a discount house. While some provide limited research and other services, their primary function is to take your order.
Most people find their brokers through word of mouth recommendations.
One way is to ask everyone you know. Once you begin hearing the same two or three names, you have a short list of candidates. Find out how the person is compensated. Traditionally, brokers made money on commission, which they earned making trades. The latest trend is to charge a fee based on the assets under management.