Get yourself a copy of the Which? Guide to Wills and Probate, which will take you through the process. I have done this twice without the help of a solicitor, except for selling the house. If the estate attracts IHT (which most don't) , this complicates things quite a bit and you may need a bit of help from a solicitor or an accountant. Bequests to charities also need special attention.
Selling the house as an executor is a standard procedure, it's just a matter of filling in the right paperwork etc.
A Probate Account might sound like a good idea but many banks don't offer this. If your own on bank or the deceased's bank don't, then it probably won't be possible. We (my co-executor and I) opened one at Lloyds and it was more trouble than it was worth, with endless formalities. All you need is a separate account in the name of the executor, with a cheque book facility.
If you engage professionals to do it, they will charge a percentage of the whole estate, which may be many thousands. I'd recommend getting the book, working out how much you can do yourself, and only using a solicitor if there are bits that seem too tricky. Just take your time. be methodical and keep careful records as you go along.
An extra tip: when phoning banks etc about a deceased's affairs, ask for their "bereavement section", where there should be someone specially trained to deal with this; they may offer quicker and more efficient service than the standard helplines.