The first step would be to go on a tour to your local bicycles dealers and take some notes. Look at their professional level and customer service. Remember you will need to go back there for maintenance after you buy your bike. Get an impression of what the dealers have to offer and ask them why they offer this to you. Write down the brands, models and prices they have to offer in your price range. You can also ask to take bikes for a test ride outside the shop, a professional shop should have no problem with this.
You are probably looking for an entry level hard tail (no rear suspension) bike from a known manufacturer (e.g. Trek, Specialized, Giant, Kona and dozen of others).
After you get a list of what your local dealers have to offer in your price range, go back home and check the internet for the specific models and brands. Mountain Bikes Reviews is a great site to read about riders’ opinions of bikes (and equipment).
Once you narrowed the list to 2-3 bikes, go back to the shop, negotiate the best price (maybe they will offer some equipment with the deal, like helmet, gloves, etc). Take the bikes to a ride again if unsure and note what feels most comfortable for you. There is really no best choice, only what feels best to ride on for you. Make sure that when you take the bike for a ride, the dealer gives you the right size and the seat is in the right height.
About the size, not all sizes created equal and this depends on the individual model. 6 feet is roughly around “Large” frame size, maybe “Medium” on some models. The only way to know for sure is measure in the shop. A professional dealer will know how to fit the right size for you, and explain how he does it.
Happy trails.