Gatekeeper - sounds like you have combination skin. Oily T zone, dry bits, dehydrated bits, ageing bits. Plus a tendency to sensitivity.
How skint is skint? I just changed one product at a time as I ran out rather than going on a massive spree. And then I knew if I thought each one was an improvement.
Starting with cleanser - bland, non-foaming, no scrubs. If CH's recommendations are out of your price range, Cetaphil comes in a big bottle and has a big fan club on here, including me. Or have a look at LRP Physiological cleansing gel or Avene Extremely Gentle Cleanser (my mum loves this) which Sam Bunting seems to recommend every single time.
Acid - look at CH's top 10, Clearasil pads are great and aren't expensive. Just pretend you are buying them for a teenager.
Serum - should be the most expensive item. Am still waiting for CH to do a top 10 for these (please, pretty please). Should have something special in it like peptides or anti-oxidants. I don't think there is a mega budget option here, maybe Body Shop Vit E serum in oil.
Moisturiser - don't spend a lot of money here. In the day it should have SPF or you need to use a separate SPF. Given the redness maybe Avene Toleriane. Nivea blue pot has gazillions of fans on here, my skin is too oily for it but it did make it beautifully soft and hydrated, plus it's cheap as chips.