GO had some Rab synthetic (Ignite?) bags cheap. Not as light / packable as down but will get you underway.
Also have a look at Field + Trek. They do a blow up mat (Gelert) for under a tenner. It’s robust, packs fairly small but is obviously a little heavy … but again it’ll get you going cheaply.
If you don’t like the idea of a tarp then look for a tent that can be pitched outer only … you’ll convince yourself you’re in a tent but really it’ll be a shaped tarp 😉
As above … remember that it’s not about taking ‘this’ and ‘that’ it’s about leaving ‘this’ and ‘that’ at home without suffering. As Matt Lee said – “Don’t pack for your fears”.