The German turntable maker Dual always used to be a good starting point for an inexpensive deck (if you’re buying ‘new’). The problem with doing that is that you can’t upgrade the deck itself - you’d have to part exchange it, if you decide later to go for a better deck.
Alternatively, you could go to a well established dealer (say, Grahams in London, Cymbiosis in Leicester, or whoever), and buy a very basic, second hand Linn LP12, which you can then spend the next 20 or 30 years ‘upgrading’.
Perhaps you’ll do well to get lots of advice here first, then get yourself and your ears to a good dealer.
You will need to re-fit phono boards for your chosen cartridge to the NAC92, whatever you decide to do.
A £300 budget means eBay IMHO. An LP12 might be a step too far, though an Axis is just possible - there is one advertised now. However, I’d suggest aiming a little lower.
If you do not still have your old phono boards, you’ll need a set - or a cheap phono stage or a turntable with an inbuilt phono stage.
£200 or so will get a Rega RP2 or (better) RP3. Pro-Ject Debut (and others) would fit the bill well too.
Cartridges may well be worn on an old TT - a suitable AT, Rega, Ortofon or Goldring MM cartridge will be needed at some stage. That’s £50 - £100, but hopefully not immediately.
A separate phono stage will cost a least as much as a cartridge. For a MM cartridge, Naim 522 boards are a good choice, but they don’t look to be much cheaper than (say) an older Rega Fono or Fono Mini.
There is an offer on eBay now for a RP2 with Fono Mini for £255. That plus an Audio Technica AT95e (£50 new?) should work well.
Or buy an early-new Rega Planar 1 Plus, which is more basic in a couple of ways but includes the Fono stage and (when new) the Rega Carbon MM.
Those Rega products all have comparable competitors that are worth considering in the Pro-Ject range.
I recently bought a Rega P1 as a back-up and singles player. £239 including cart was what I paid. You’d be amazed how good this sounds - not too far off my P3. Don’t buy the Plus as you can’t use it without the phono output which is reported to be not v good. Get the Fono Mini instead, less overall cost anyway.
Linn LP12 for £300? Not possible on any level. Have had Linn Axis and Rega Plana 3, either would be ideal. Buy on ebay and take a chance on one. Or buy a new lower model like a RP1 as suggested. Most turntables at £300 new will be okay. Just don’t expect the earth. I have a Thorens turntable as well as an LP12. They are worth a shot as well, especially with your olive system. Will look great.
Why do you want vinyl? It’s popularity arpt the moment is predominantly due to it being fashionable, with recent vinyld often derived from digital recordings! In my view, unless you have a vinyl collection you are wanting to play it would make more sense to think what cpyou could do to improve your streaming system. Streaming with good recent DACs at last has realised the sound quality claims that heralded the introduction of CD, while vinyl to get close seems to require huge outlay, at least that is my impression from posts on here, and certainly I’ve not heard vinyl as good as good digital. (A caveat: not all digital has been recorded well, in particular some having been bastardised by artificial compression, apparently in the interests of radio playability. But then not all vinyl was recorded optimally either.