Get them to sign a receipt of sale (AA do one online that you can print off) do a copy for them and one for yourself, make sure you put the time on it so if they do get a ticket you have proof it was them.
The v5 transfer can be done online as long as it’s between 7am-7pm, if it’s after then just do it next day. The new logbook is normally with the new keeper within a week, you’ll get a confirmation of vehicle transfer and any tax refunded.
There is an option to have email copies of the logbook transfer sent to both parties online.
Give them the v5/2 (green slip) as they’ll need it to tax the car, you can destroy the rest of the v5 but I always wait till Iv got the confirmation through the post just to be absolutely sure.
Do none of the above until the funds have cleared into your account and make sure you check your account and not just going off their account that it’s been sent, if they’ve already transferred £150 then it should be recognised by your bank and the remaining funds should clear straight away.