Just been accepted, what next?

Malmo

With regards to conveyancing quotes, obtain like-for-like quotes for a number of solicitors and/or licensed conveyancers that can do the conveyancing tasks for the property you wish to purchase. Then choose one that you are comfortable with. Avoid solicitors recommended by the vendor's estate agent as the agent will receive a commission / referral fee / kickback, which will inflate the cost to you.

Have a look at this article for a breakdown of the solicitor / conveyancing costs that you should review and query when comparing quotes.