FAA has several aviation classifications. Part 103, Light Sport, and (? Regular airplanes) general aviation.
Part 103 of FAA regs details ultralight aircraft.
Simply, part 103 means aircraft under 254 pounds weight, 62 mph top speed, 5 gallon fuel capacity, single place, etc. No pilot license required. No physical required. No "N number" (registration). These have other limits, such as can't fly at night, etc. As well, they have regular limits that larger airplanes/pilots must follow, like airspace, traffic, etc.
A true part 103 aircraft will be advertised as part 103, and will be within the limitations. Many, many, many of these have been sold since the 80's and lots of them are still manufactured. Materials and designs have modernized, but some look like they're as simple as the Wright brothers' Flyer. For example, Quicksilver ultralights once outsold Pipers, Cessnas, Beech, etc. all TOGETHER, and many are still in service. Mine is a 1983 vintage MXL with a 35hp Rotax 377 engine. It is an extremely stable and very mild mannered basic airplane. I'm 5'8" 185 and my aircraft will JUMP into the air in less than 50 yards and has WAY more power than I ever imagined and will climb at 800 ft/min, has 14,000' service ceiling, with about 55mph top speed, 100 mile range.
There are now quite a few manufacturers with LOTS of different models & features. Again, please see "Barnstormers" and other sites for sales ads. "SearchTempest" will also give you EVERY Craigslist ad for any item you specify in every state you specify. There are other airplane sales sites.
A single seat part 103 ultralight will be very basic flying, but they can be amazingly expensive, if newer. Older, used aircraft are perhaps a more economical way to go. A friend of mine (almost 80 yrs old, used to fly) is currently looking for a used acft. He remodeled a trailer to haul one, and has $5,000+ ($7,000 with Trump bucks, if it comes) in hand and will buy something pretty soon. He also will need cataract surgery in Jan/Feb and STILL wants to fly. So it is easily possible to get a decent used UL for about the same price as a motorcycle. He says, "If it don't fly... don't buy!" (in other words, DON'T BUY some project plane. There are a bunch out there, that some guy bought a kit and thought he could put together in his garage... and never finished.)
There are quite a few companies who support (with parts & maintenance) the Rotax engine, which is no longer manufactured.
Quicksilver acft Co (California) went out of business a few years ago, but a guy in Lousiana (Air-Tech, Inc.) bought the entire inventory of parts, hardware, etc. I mean EVERYTHING and has all the parts for every Quicksilver model ever made.
This is just an example. There are LOTS of other manufacturers and models of true part 103 UL acft. Some of them are designed to fold up/unfold quickly to be transported on/in a trailer.
My acft lives in a 20' box trailer, and takes about 2 hours to set up from trailer-fly. Other makes/models are WAY easier/faster.
Its a PITA to set it up, but I don't pay anything for hangar space (up to $225/month around here.) Ideally, I would have a small airstrip with a shed/pole barn and store the airplane set up and ready to fly at all times. UV light degrades dacron sails (wing covers).
Light Sport class is the next higher/heavier class. Two-seat ultralights fall into this category. A 2-seater is bigger, heavier, more powerful than a true part 103, and has different rules.
Light Sport doesn't mean small, or cheap, however. You can EASILY spend $100,000 here.
General aviation (Cessnas, other light aircraft, etc) is a whole nuther class with its own rules.