A bit of general information:
In terms of picture quality, there are basically 4 levels of screen definition available:
1. Standard definition. (SD). Such sets are fine for smaller screens (and people on tight budgets).
2. HD-Ready. Such sets can display pictures from external sources (such as Blu-Ray players and Sky HD boxes) in HD but they don't have a Freeview HD tuner in the, so you can only watch Freeview channels in SD.
3. Freeview HD. As above but with the ability to watch Freeview channels in HD.
4. Ultra HD (or '4K'). The best image quality but expensive and only really worth considering with very large screens.
With the limited information we've got so far though, this is well worth considering (with Freeview HD, catch-up apps and the ability to record to a USB stick):
https://www.richersounds.com/tv-projectors/all-tvs/sony-kdl32we613-blk.html
(It's also from an excellent manufacturer and a highly-respected retailer)