Iceland inverts the usual rule. In most countries you save money by doing things yourself; here, guided tours are often the cheaper and safer option, because the alternative involves a rental car, insurance that excludes ash and sand damage, and winter roads that close without warning.
The season decides almost everything. From June to August, rent a car — you get twenty hours of usable light, clear roads and the freedom to stop at every waterfall. From November to March, book tours, and put the money you would have spent on the rental into a glacier hike instead.
The things you genuinely cannot do alone
Glacier hiking and ice caves require a certified guide, both legally in practice and because crevasses are not visible from the surface. Silfra snorkelling needs a dry suit and a licensed operator. Those two are the highest-rated activities in the country and they are where your budget should go first.
What to skip
The Blue Lagoon, on price and distance grounds — Sky Lagoon is better and closer. Also skip any northern lights tour without a free re-try guarantee, because roughly a third of departures see nothing and you want a second attempt included rather than sold to you again.