Ahhh, that makes more sense! Sorry, I/we thought you were buying the house you were already living in - durrrr.
Then you can probably wait on the lawyer thing. You will have to get one, though, when you are ready to buy as the conveyancing (the progression of the sale) cannot be done without one. The lawyer takes care of all the legal issues surrounding the sale. Don't worry, you would only have little contact with your lawyer, as it's the estate agent's job to chase them and progress the sale. Most agencies will recommend a lawyer when you're ready to buy if you don't already have one. However, a chain estate agent will likely have their own conveyancing firm that they use - which does NOT mean this is the best choice, but more that they get referral money for using them! Again, I (my husband, actually) can recommend some firms that I know from experience are good, if you would like.
Like I said before, the mortgage is really the first step. Agencies (probably especially now) sometimes don't want to even talk to buyers until you have a mortgage agreed in principle. Lots of estate agents have an ISA working in-house, so that's useful too.
I guess step 0 on the list should've been RESEARCH. Look on the internet. When you find stuff you like, contact the agent. Looks at several agencies' stock before making any decisions.