Title Work is the whole process from beginning to end involved issuing title insurance. It starts with a "title search", which is examining of the title in question to ensure the seller is the actual title owner and to determine what, if any, liens are on the title.
In a real estate transaction, once the Title Work has been performed, then there are usually 2 types of title insurance that are issued:
Owner's Title Insurance: Insures the owner against losses due to title defects. Typically the seller pays for this. As for the fee, the charge is usually based upon the sales price of the property, and can vary from area to area.
Lender's Title Insurance: An insurance policy that protects the lender against claims and losses that may arise if the title is unmarketable or defective. Typically the buyer pays for this.
In most cases, the seller chooses the title company -- but this can be negotiated in the purchase agreement.
As for how to best choose a title company, often times the attorney or even the listing agent representing the seller may be a title broker to have ownership in a certain title company, and may recommond you use a certain title company. Make sure to ask if they have an ownership interest.
Good questions to ask a title company: 1) How long have you been in business? 2) Have you had any claims against the titles you have issued in the past? 3) How often do you reconcile your escrow accounts? 4) Do you disburse on transactions before verifying receipt of good funds from all parties? 5) Is my whole closing process being insured by your company, or only the tile policies?