Since you seem to be familiar with the internet, you could start there or start asking around - neighbors, friends, relatives, co-workers. Ask them if they sold or bought a house recently and if they liked their agent. Or you can check the internet pick a few agents. Look into their about me section and try to get t feel for the type of person that they are. If you only go by how many listings they have, you may find disappointment down the road. I once had seven closings in six weeks and then nothing for over a month. If you had check during that month, I wouldn't have looked very good to you at the time.
Tell the agent that you are interviewing several agents and that you would like to set up an appointment for them to come to your home. Once they get there, you can get to know them a little better. Be careful that you don't place too much important on commission amount because as with anything, you usually get what you pay for. It is much more important to ask what type of marketing they will do for your property.
As far as big company? There was a time when that was really important, but with the advent of the internet, I personally don't believe it is as important - and I work for a very big company. The agent can make or break a deal. You want to make sure that they stay on top of things. Make sure they check agent ID before allowing a showing. Ask them how often they will keep in touch with you even if there is nothing new to tell you.
As far as the timeline, once you have chosen the perfect agent for you, you will be asked to sign the listing agreement. Make sure you thoroughly understand it before signing. Ask questions. Then do everything your agent suggests. If he or she tells you to paint, then paint. If he or she tells you to rent a storage to get clear out your home, then do it.
Remember we do this for a living so we know what prevents homes from selling. I know I have mentioned this before on Trulia, but I'm going to say it again because it is sooooo important. We are in a beauty contest right now due to the large inventory. We have to go one step above the rest to appeal to the buyers.
My hubby, bless his heart, once told me that if there was a two-foot square empty space in the room, I would find something to put there and he is right. I prefer my home to have things around me that have meaning. However, I know that if I were to put my home on the market, I would have to rent a storage unit and empty it by at least half. It is not junk or clutter. These are just things that we get used to living with. The buyer will be turned off by it.
And last but not least, I'm not sure of the current market conditions where you live, but where I am, we need to give the listing a six month contract. Agents are spending more and more time and money to help their clients and they want to know that you will commit to working with them to get the home sold. If you turn into a seller that wants to agent hop every couple of months, you will not get a good quality agent and the buyers will start to wonder what is wrong with the home.
Good luck to you.