Ok, so basics:
First there's a kind of in-between point for buying new/second hand. You can buy reconditioned, you can also buy rejected stock. You'll find businesses that specialise in this on eBay etc. Rejected stock will just have a chip on it or something, companies buy pallets of the stuff at auction and sell it. Often has some kind of warranty... I bought my hob off one, but fridge was from John Lewis iirc.
Washing machine, generally buy new. That's an open slot, so you should just be able to get a normal free-standing one. Double-check measurements, but should be fine.
Fridge, I'd stick with what they did. New is generally better, but they do get expensive fast. Depends how you feel about spotting a good deal, and whether you've got a mate with a car. The problem with them is they can be quite easy to damage in transit.
Oven... You have choices here. Think you've got a gas outlet there, so that's a possibility. It would be reasonably easy to switch from free-standing to fitted. I'm guessing that slot is a standard unit width, so all that needs to be done is stick an oven unit in, plus a bit of extra worktop. Although if you did that it would probably be worth replacing that whole run of worktop. The wiring might also be an issue for new stuff (because it's bloody daft having wiring right behind a hob, regs may have changed). Generally it's fine to keep things like outdated wiring if you're just swapping like-for-like, but not if you're redoing something. That wiring should be very easy to re-route though.
As above it would also be worth getting a cooker hood in above that, though personally don't know how easy it is to arrange the ducting to the outside (you can also get recirculating ones, but less effective).
Any half-way competent joiner should be able to advise you on this, and it shouldn't be super expensive. It's not more than a day's work really, although would need to call in a gas safe plumber and maybe an electrician.
The easiest/cheapest solution would be to get in an electric freestanding stove, that just needs to be wired in. But redoing the worktop potentially gives you the option of a nice big gas hob. Depends what you want to spend really.