Home DIY

That front door/entrance way from outside would be my 1st job, make it secure from previous tenants getting back in (happens way more than you think, had it only happen to me once personally, but numerous mates numerous times) and just looks like a cheap modern bedroom door type affair, not really up to 'securing you from outside' in either warmth/sound/assholes.

Bathroom/kitchen. Unless you have to live in it immediately would tackle those 1st and just chase out where all the services come and go from, got to be some re jig worth doing as both look pretty terribly laid out (looks like former terraced house/home thats been quickly made into flats in the 70's).. Think about extraction too, many older/conversions don't have adequate ventilation in bathroom kitchen for steam + smoke + cooking grease so the whole place gets disgusting quickly. Access to outside walls and ability to core drill them is harder than you think.
In our current project gonna have to hire a lift just to put a few vents in roof, cheaper than scaff, but still hundreds just to get on the roof, then install as many vents/boiler vent pipe/aerials/dish/gutter repairs as possible in the 4 hours we've got it for. I'm sweating just thinking about it.

Rest of rooms look OK, would just walk aroud each one with a cup of tea, clipboard and a screwdriver and poke EVERYTHING.
Get an electrician in, pay and do a test on what you've got, so you know if you'll need a partial rewire or just a new consumer before you do much else (no point plastering a wall only to find your gonna have to run new cables in it a month later, done that one about 5 times now FML).

Check with upstairs and downstairs neighbours for general arsehole'ness (if they are, just sell it and move, as the new guy, you won't win any arguments), leaks and noise. Most often there will be a noisey floorboard (yours or their's!) that you'll only discover when you've finished the place, and you can hear them moving around.
Consider insulated plasterboard/other options around party walls and exterior walls, energy prices gonna keep rising, worth doing something while your at it.

Just bought another new tool, milwaukee RO battery sander. Why the hell haven't I owned one for the last decade, makes life so much easier, and much more gentle than other sander types while still actually removing material. Total lifesaver.