Your advice is excellent, but I do want to point out that renting a U-haul pickup truck or van for one day, in-town, can be worth it. Check if the total price of the rental + the used furniture is still good, and which kind of hassle you prefer. If you're lucky/not picky you can get a few secondhand pieces in a day or a weekend and make the rental cost less of an issue.
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Peak strat would be to rent a U-haul for the weekend after graduation in a university town, and drive around the student district with a sturdy friend, celebrating Hippie Christmas.
However, like you said, learning to fix furniture is a huge step up, too. Especially if your furniture is old but not priceless 14th century antique, there's not much trouble you can get into replacing screws, adding shims, tightening loose joints--nothing like sturdy furniture to make you feel like real people.