Rob,
congratulations on taking a first step on the hifi ladder. Seems very few people today seek out quality music playback over crappy mp3 files.
Unless you have also inherited a big record collection I would not advise you to go down the vinyl route. Yes, vinyl at it's best does sound better than cd's but it comes at a price premium. Given that your funds are limited, I would not be investing in vinyl (or cds for that matter, as the latter format also has a limited life expectancy).
Instead, I would subscribe to Tidal (or similar) and use your funds to get some decent speakers and amplification. A monthly subscription to Tidal costs about the same as one vinyl album, but will give you access to a huge collection of uncompressed music files. You can even download these files to a phone so that you can listen on the move.
A cheap device like a Chromecast Audio (30 quid) can feed into your system and will give you a quality of sound that you may not have heard before, and can probably be used with the system you inherited. When funds are available, I would look at something like this: https://www.richersounds.com/yamaha-...amplifier.html
This is a digital streamer and amp combined. It sounds fantastic, and the Music Cast system and app is great too. You can play music wirelessly from your phone, pc or tablet.
Whatever path you take, good luck!
Geoff