I think that, if we define a personal computer as a machine that is designed for a single interactive user, the LGP-30 would be a good candidate. It was not, however, a home computer.
For me, a personal computer needs more than switches and LEDs as its UI. With a serial port, a terminal, and a monitor program in ROM, the Altair would qualify.
Not as powerful as a PDP-8, but less than a tenth of the price.
It was the perfect aspirational project for the electronics hobbyist community of the time.
The fact that you could barely do anything with it wasn't the point. It was a real computer you could set up at home and use without time restrictions or hourly billing.
The S-100 bus market turned into a preview of the PC market. S-100 systems soon sprouted real terminals, floppy drives, and workable memory, and began to appear in the offices of accountants and other non-tech professionals.
The IBM PC probably wouldn't have happened without it. It normalised relatively affordable computing, and the idea of a third party market of expansion cards on a standard bus.
The video memory would either be in the computer or the terminal. At least if it were in the computer, you could use it for other stuff.
It had a keyboard and video board, rather than a terminal. The monitor was open chassis to boot (ah the old days when we didn’t protect children from lethal electricity).
It had a ROM monitor and cassette tape. You had to type in (in hex) a short machine language program into the monitor to load BASIC from a cassette. We simply never turned it off.
I tried ti enter the bootstrap through the front panel once, but I made some mistake, and it didn’t work. It was an awful enough experience I never tried again.
The serial port was its own separate board. https://www.youtube.com/watch?v=RaYTd3dbXeM
There were two very clever I/O ideas that emerged for the Altair: (1) A radio on top of the housing would pick up a signal, allowing audio output! (2) A cassette tape recorder could be used as an external storage device, though I forget how it interfaced... the serial board, I think.
The Altair, in 1975, was the first commercially successful personal microcomputer.
https://en.m.wikipedia.org/wiki/Datapoint_2200
The 6502 line came out Motorola's failure to "indulge" their employees in a low-cost 6800, thus unintentionally fathering MOS Technologies.
https://en.m.wikipedia.org/wiki/MOS_Technology_6502
The 6502 was extremely inexpensive. The first implementation was the KIM-1, so this is the first on that side.
The Wang 2200 looks most like we'd expect a personal computer to look like, but the price range was not home-friendly (~$50k today).
Apple had the II in the late 70s, and before that was the Altair.