What's the best way to waterproof a basement?

It really depends on where the water's coming in, you know! If it's from the base or the sides, the solution changes quite a bit. Waterproofing membrane is good stuff, but it's a pain to apply if you want to do it yourself - gonna be a lot of work! Resin injection is easier for DIY, you inject it into the spots where it's leaking and it expands, seals everything up. The cheapest thing really is to first check if it's not an external drainage problem - sometimes the water's just running too close to the basement, and you can fix it with a gutter or redirecting the flow! If you've confirmed it's actual infiltration, I'd start with injectable resin, which is way cheaper than redoing the whole waterproofing with membrane.

The most important thing is figuring out exactly where the water is coming from - whether it's seepage through the walls, rising damp from the floor, or even condensation, because each problem needs a different solution. If it's moisture from rising damp (that "sweating" on the walls), injecting hydrophobic resin into the bricks is way cheaper and more effective than a membrane. Now, if water is actually getting in through the wall when it rains, then you really do need a membrane or epoxy sealant on the inside, but ideally you should also check whether the problem is coming from clogged gutters or poor drainage outside - sometimes a properly installed drainage pipe solves everything for a fraction of the price.

Resin injection is generally more cost-effective than membranes if the humidity is coming from the side walls, because it tackles the problem at its source by sealing the pores in the concrete or brick. But if water is rising through the floor (capillarity), neither of these two really solves it well - in that case you actually need to install a chemical damp-proof course or an external drainage system, which is expensive but it's the only thing that actually works.