If you want to play 78s you'll need to really think about what you're after from a turntable.
Most serious hifi nuts who play shellac records use a specific cartridge (the bit that holds the stylus on the tonearm) which is designed purely for 78rpm 10" discs. Obviously you'll need a deck with the correct speed changes too - my own, a Linn Sondek, only plays 33.3rpm unless I fit an adaptor to it to play 45s, but I rarely need to do that so it doesn't bother me.
It's not just the turntable either : you'll need an amp and speakers too.
I would recommend you go down the vintage used route.
There's plenty of well maintained bits on eBay and quite a few specific dealers, including one based in Bordon not far from where we met up for lunch that day. They're only on eBay now - hifihangar is the seller name - but they often have really good gear.
If you do decide to go down that route, let me help you as there are some bargains to be had out there, especially on GumTree.
I bought a Pioneer PL-12D for a tenner about three years ago.
It was the best selling deck in the world during the 70s and is a brilliant piece of kit and most people would stop there and never need to get anything better .. not unless they're anoraks about it all, like me