Early on I changed the thread title from 'owned' to 'owned or used', so I've added this post, to fill in the extra details. I've already said my first owned computer was a self built MK14 (photo in OP was NOT the one I built, none of the photos are of the machines I actually used, stock ones used).
The first "computer" I remember seeing in real life (which was not really a computer, but from that era, it just about counts as one), was an all valve/tube (but it did have one Germanium transistor in the voltage supply circuitry), was an Anita calculator, probably the first one, which was a MK8. But I did NOT use it, so it does not really count. (But later on I did play around a lot with an early, Toshiba calculator. It had lots of TO-metal-canned ICs in it, and could flash its nixie tubes in a really fascinating way, for lots of seconds, when you gave it a massive calculation).
It looked much bigger than the picture seems to show. It was the size of a very large typewriter.
Ignoring calculators and a programmable calculator (Texas Instruments SR-52), my first access to a computer, was an ancient all TTL (mini-computer like) massive desktop Wang computer. Called something like a 2200. Similar to the picture below (but I remember it being all white in colour, except the top floppy drives).
I use to love programming it (for fun) in its built in Basic language.
Later I had access to (not necessarily in accurate time order, as I can't accurately remember the exact timing sequence):
Commodore Pet, nice for programming in its built in Basic, and even 6502 machine code.
ASR-33 mechanical terminal + paper tape available + modem to talk to a mini-computer, which was probably one of the ICL1900 series, computers. If I remember correctly the language used was CECIL. An early, assembly language like programming environment. One step above machine code.
Commodore 64, which was mainly for gaming.
BBC model B microcomputer (later with floppy disk, external add on, and one or more extra Rom/EPROM chips)
Mainframe computer, made by ICL, 2900 series, in the classical format of the time. A huge (air-conditioned room), with massive cabinets. A very fast line(page) printer (it could print things out, amazingly quickly), many computer operators. Access to the computer was by video display unit terminals (there were VERY few of these) so access to them was VERY rare, printing terminals with built in keyboards (probably Dec). Very rarely access (if you could use one of the more 'modern' terminals, that was the preferred solution), via punched card (which I remember doing).
My first (owned) PC, was an Amstrad PC1512, with colour screen (EGA if I remember correctly), pair of floppies, 20 megabyte external hard disk (internal ones were possible at the time, but I wanted to keep access to two floppies, for easy copying of them). 8086 at 8 MHz, 640K ram (if I remember correctly, but it could of been 512K).
I actually designed schematics and PCBs on it (as well as all sorts of other things, I did with it). I had access to a (long term borrowed) Rowland Plotter.
Turbo Pascal was amazingly fast on it. Eventually I used C as well (Turbo C).