I first saw a PC in 2nd grade at my school, and was instantly captivated by it. Trough pressuring and a little emotional blackmail I got my parents to source me my first x86 PC - a 486 class machine built by a romanian company called REL Computers (they're still around, they just don't make PCs anymore). It was a 133MHz Cyrix 5x86, VIA chipset board, 8MB of ram, Cirrus Logics PCI video card, and 800MB Quantum Fireball HDD. No sound card, no CD-ROM drive. It also came with a 14" color CRT monitor and an OKI Microline dot-matrix printer. About the CPU - yes, I know, these are considered very rare now, and yes, it's possible it was actually a oveclocked 4x 5x86-120GP, but whenever I try to picture it in my mind I remember a green heatspreader with Cyrix 5x86-133GP written on it and a fan on top witch I had to clean two-three times a year and even replaced once. I got the machine for my birthday in October 1995, and have used it until late 1999, when I upgraded to an AMD K6-II.
I don't have any pictures of my first PC, but the case looked exactly like this one (sans the CD-ROM drive):

The case was made by Sunshine computer. I've been trying to find one like it, but I could only get a hold of the slightly newer model. I played the shit out of Dune II, Volfield, Jazz, Doom, Supaplex, C&C and lots of other 90s games - good times 😁
The 586 went thought several upgrades - first the ram was expanded to 16MB and the Quantum Fireball HDD was replaced with a 2GB Western Digital (1996). In 1997 I expanded the ram to 32MB and bought my first sound card, a Yamaha OPL3-SAx board made by some chinese company ( Genius SoundMaker - still use it in one of my builds). To go with it, I borrowed a 24x creative CD-ROM drive from a defective PC my dad had at work. In 1998 I got it a voodoo 2 witch allowed me to play quake (GL_Quake - regular quake still ran rather poorly) for the first time at acceptable framerates (not great, but VERY playable). All upgrades that went into the PC were purchased by me, using pocket money saved up from school lunches and some money I earned working part-time at a PC repair shop in my home town.
The K6 was purchased by my folks, as a surprise, and required my old 586 as a trade-in / rebate. Back then, they asked me "If you could get a new computer, what would you like to have in it?" - and of course, I asked for the then newly released Pentium II, a Riva TNT, 64MB of ram and a 4GB hard disk drive. What I got is what my parents could afford - a 450MHz K6-2, 64Mb of ram, 4GB HDD, and a VIA MVP4 motherboard with on board sound and video. I was both excited and disappointed by the new machine - sure, the CPU was WAY faster than the 586 - but the on board sound was of poor quality, and the on board-video would perform about as well as my old Creative 3D Blaster II on the 586 (trident blade 3D - not a bad card of an on board solution, did Quake 2 in openGL at 640x480 flawlessly).
I turned it on, expecting all my data and my 3D Blaster to be inside - they were not. Of course, when my folks told me what happened with my old machine, I threw a fit. For the Voodoo 2 alone they could have gotten the motherboard and ram in trade (yes, 3D cards were THAT expensive back then in my country) but my parents couldn't really be blamed, because they had no idea about the value of PC hardware and what was inside my computer. I thanked them for the wonderful gift, and politely asked them to take me to the shop they got the new PC from so I could re-negotiate the deal, and get the stuff off the HDD from my old computer. They didn't get the machine from the shop I usually worked for, so I wouldn't find out about the surprise. The other shop had appraised my 3D Blaster at 10% of it's real value, and had made my parents buy another AT case and PSU when there was in fact no need to. After I threatened to return the new PC, the salesman offered to return my Voodoo2 and the Genius Soundmaker, but also replaced the 450MHz K6-2 with a 400MHz K6-2 and the 64MB stick with a 32MB one. I didn't even mention the fact that there was no need to make my parents buy a new AT case and PSU.
In time, I added more ram to the K6 - it had 128mb at one point. I added another voodoo 2 (also a creative CT6670) - the only possible upgrade path since the motherboard had no AGP port and PCI cards like voodoo 3 and geforce 2 cost about 50% more then their AGP counterparts and were very hard to find. The CPU was overclocked to 450MHz and was used at that frequency for at least 2 years.
Most memorable games I played on my K6 were Quake 2, Unreal, C&C Tiberian Sun, Dungeon Keeper 2 and Homeworld (my favorite game ever).
Later in ~2002-2003 I replaced the K6 with an 850MHz AMD Duron / KT133 mobo (Matsonic I think), ATX case+psu and a radeon 7000. Kept my ram (witch by then had been upgraded to 128MB) + 4GB samsung HDD (witch I still have! an the thing still works perfectly!) and of course my 3D Blaster Voodoo 2 SLi setup. I still have the Voodoo 2 cards, the SLi cable and the pass-trough cable. I worked so hard for the first voodoo 2 card, I couldn't bare to sell it, and never have. The two voodoo 2 cards now sit in my P3 V2 SLi win98 box and see weekly use.
After that, I went troughs so many PCs - KT333 / XP 2400+ / Radeon 9000 - later upgraded to a Barton 2600+ and a 256Mb FX 5200 (back then i was under the impression that more vram = faster video card). I upgraded this when I won a Gigabyte nForce 3 board in a Red Alert contest when I was 18 and traded in my barton + mb for a socket 939 Athlon 64 3000+. A few years later, I upgraded again - this time to an Athlon 64 X2 3800+ on top of an Nforce 4 (Asus I think) with an 6600GT. Shorly after I upgraded to a 6000+ with a 7900GT (AMD fetish, I admit it).
My first intel PC was a Q6600 I got as a Christmas present (the CPU only) from one of my uncles. Again I traded in the old CPU and mobo for a LGA 775 MSI P35 Neo-2, and sourced me a built by nvidia 8800GTX sample from a friend who worked at a romanian PC magazine. This machine lasted for a while - it got 4GB of ram, a Q9550 and two radeon 2900XT furnaces (lovely cards - quite a bit cheaper than the 8800GTX witch died after a year of use and performed similarly).
The most expensive PC I ever owned, and the only top of the line PC I ever bought was a skt 1366 core i7 with 6GB of Corsair XMS3 DDR3, a GTX 480, Antec truepower quattro 850w, Thermaltake Shark all aluminum tower (witch I still have) and twin 250GB HDDs in raid. Other than that, I had a Phenom X4 960, a FX 8230, a i5 2500k then 3570k.
The last desktop I owned was an LGA 2011 i7 3820 / 16GB Corsair Vengeance, two R9 280x cards in CF (initially two 7950 cards inherited from the i5 above), 128GB Samsung SSD, 2TB WD caviar green, Gigabyte X58-UD3, OCZ Fatal1ty 750w psu all stuffed in a Cooler Master HAF XB. I sold that last year so I could go mobile (I spend at least 4 nights a month at the hospital).
Still have a few pics of my last desktop:

Same machine but with 3x Sapphire HD 7950 in it for funzies 😁

My current rig is a Asus ROG G751JY (i7 4710HQ / GTX 980m). I do miss tinkering with and customizing a desktop, but I prefer having my machine with me in the on call room.
tl;dr - started on a 586.