if you want to super save some money for a budget build, look for reconditioned office boxes on ebay. Dell optiplex 990 with i7 2600, 4gig ram, 500gig drive for £150.
slap in a 1050ti - or something that doesn't need a PCIe aux 6pin or 8pin power and you're laughing.
there are 6pin to sata power adapters if you step up to needing extra juice - just be aware that these are office boxes, so if the PSU goes pop; it might be a custom shape, and pin connection on the mainboard.
i run a small formfactor Dell optiplex 990 i7 2600 (will 16gig ram and SSD) myself as my "steambox" in my mancave - it's getting a bit old and creaky with the GTX650 i've got in there, but its fine for the 55" 1080p display it's running. however, i'm stuck with low profile graphics cards because its the small SFF case. still got an SSD or for a 3.5" drive, and slim optical drive slot if you want that. i've also got other small formfactor 990's around the house as netflix or whatever boxes, just running off the onboard intel graphics via Displayport-to-HDMI adapters.
the smallformfactor optiplex 9010 & 9020's were a no-go for me, as the x16 PCIe slot is at the bottom/farside of the case and cannot accommodate a dual slot cooler like the SFF 990 could. however, i did have a pair of 9020's that i couldn't fit a decent GFX card in - because of the space problem, so , i gave to a friend of mine so he could harvest the i7's and ram out of them.
if you get the mini-tower versions of these office machines, you should have no problem with space - just be aware that as these are office boxes, you may not have the watts from the PSU to drive anything too big graphics card wise. I picked up some HP deskpro tower boxes - gen4 i5, 8gig ram, slim DVDrw, Nvidia NVS310, for £40 each, and no PCIe aux power, so at the time was limited to GTX750 graphics.
for my main box, i run a Dell precision 5810, with a xeon E5-1650v4 cpu, 16gig DDR4, nvidia Quadro M4000 8G (gtx970 equivilent)
my wife has a Dell precision T3600, 16gig DDR3, xeon E5-1650v2 cpu, nvidia quadro M4000 8G
my homeserver is a Dell Precision T3610 with 64gig DDR3, xeon E51650v3 cpu, nvidia NVS315, dual10gig nic, dual SAS/SATA drive controllers.
all for zero cost - all office cast offs. where i did have a cost was retro fitting all the machines with drives. SSD's across the board apart from the homeserver's storage drives.
Anyway, where i did spend money when i did a build, was on the GPU - always looking for the sweet spot of price vs performance.
if you get a cheap GPU, it'll run out of power long before your CPU starts getting stressed, so spend there. DDR3 ram is pretty affordable these days - seems to have taken a bit of a drop in price recently, and you'll not really notice the difference between DDR3 and DDR4 in real world applications - hence the i7 2600 is still a good chip to run, even now.
but yeah i agree, also don't skimp on your PSU if you need to buy one. you may find that a good one will outlast not just this PC build, but like your monitor, it'll be there for your next pc build, and the next etc...
i've had good experience with Silverstone/coolermaster PSUs, Gigabyte/Asus mainboards, EVGA/Gigabyte/Zotac graphics. Samsung/Intel/Kingston SSDs.
i've not had good experience with Corsair's 650W PSU's. i've had two die - after the PC's original Thermaltake PSU died from many years of service, running my old storage server 24/7 (AMD PhenomII x6 T1055, 8gig ram, 8x 4TB, 2x 2TB) - currently running a silverstone 700Watt iirc
i've also not had good experience with MSI - but they are still around so i guess it was a limited case with the gear i was buying at the time, and the subsequent experience of trying to get it fixed or returned. even so, i'll never personally buy MSI again.
but yeah. sorry got a bit carried away there. hope some of that is of use.