ok, so we bought a right doer-upper. We spanked everything on the deposit so had to move in and save to get work done. I can say that trying to rewire or even just install some LAN after moving in is a right PITA. You end up with a slidey puzzle of storing furniture and boxes in each room in turn and everything gets dusty and the work costs you 2-3x what it would if you gave the sparky an empty house to rewire in one go.
Aim to rent for a month at least, if not two. Get all the wall paper stripped, rewiring, new plugs, new mainboard, LAN, plumbing alterations and new rads, boiler, carpets replaced/shampooed whatever. Make your list and move once the chaos is done. Don't do what we did if you can possibly afford it. While the floors are up install acoustic mineral wool into the intermediate floors and get the loft insulation up to regs too (or do what I did and improve it as best you can while still getting boards down over it onto the joists - even that made a massive difference getting rid of the old itchy filth and putting in proper Knauff between the joists)
I am still installing LAN as a DIY project (couldn't afford to pay sparky, and I was given a drum of cable which helped). It's fine, just juggling it with wider DIY and the baby is not simple. Fun learning experience and well within a DIYer. I would not do my own electrics though. You can do first fix (running cables) ok if you know the circuit requirements, but you need them to do all 2nd fix and wire the mainboard.
TBH best just get them to do the lot.
Specify they must use wall chasers and not just kango your walls blind. Trust me the latter does not give as good an outcome. Also consider specifying all cabling in conduit (even if concealed in wall) for easier future alterations.
A standard plug socket will house 2No RJ45 end modules, and a dual socket will house 4No. I use the LPT modules as they are smaller so are easier to fit in the backbox and manouvre the faceplate into position. Cablemonkey is brilliant for cable. Not cheapest, but reliable quality. Recommend the orange 6a LSOH and BC2a fire compliant varieties for no smoke risk. They do U/FTP and F/FTP either are fine, the latter is best if you can afford it. Don't use STP or patch cable for permanent wiring. That stuff is for bendy user cabling with crimp fixing onto standard male RJ45 terminals. The solid stuff is what you put into permanent wall female sockets.
Whoever does the install make sure they follow the guidance on min bend radii for the cables.