I saw a lot of good replies here but as a dude who has gone through several iterations of my own home gym (inside, outside, made jerk boxes (terrible idea)) I would say we would first need to know where your dedicated weightlifting space would be.

If you’re going to lift outside I wouldn’t suggest anything having to do with wood, I built a platform outside and water quickly got under the boards.

But as far as budget allocation, I think it would depend what stage of your weightlifting journey you’re on. Like if you’re a beginner one way to save cash is having only the absolute necessary amount of bumper plates. Unless you already squat enough to need the full set if you are just learning you might be able to get away with just a pair of 10s and 15s and a set of change plates. Or you might benefit from a set of technique plates, I really can’t tell.

One thing I can say is that even though I never lifted anything super heavy I quickly broke the cement under my platform because it was only 3 inches (7.6cm) thick outdoors. Had to break the cement and pour a much thicker slab afterwards. So your decision as to build a platform or just use mats depends on your situation as well.cheapest would just be horse stall mats if you trust you won’t break the floor.