If you're pushed for budget I'd spend it on the razor. Great soap and a good brush do make a big difference, but you can compromise these and still get a decent shave. Not so much with the razor and honing. When I first started I used a broad soft paint brush straight out of the garage and some very cheap soap. Not the best, but did the job and what a great feeling it was to get a good brush and soap for a birthday.

A strop is another question. After leaving my admittedly cheap and narrow strop in a hotel room (top tip, don't hang them on the back of a door...) I made one out of string and a leather scrap for next to nothing and it's even better than the old one. So you don't have to spend a lot, but the razor is where to really invest in my view.