I'm the same.
I bought this in 2015 and it still works fine now: https://www.amazon.co.uk/gp/product/B00JSLN96E/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1
Very minimal lag, hardly noticeable. Quality isn't great but you're streching 240pish images to 1080 so it's always going to look crap without spending hundreds.
Totally worth a go!