I'd recommend RC2014/Small Computer Central kits
After a break of many years I've got back into soldering, courtesy of Small Computer Central and RC2014. Whilst this is still computer based, there's something compelling with working on hardware rather than Yet Another Software Problem. I'm enjoying this to the point that the next stage is a (fairly simple) circuit from scratch.
SCC kit tends to be 80 pin, RC2014 is mostly 40.
This is almost all through hole, and tolerant to a moderate extent of inept dabblers. I've just built one of the SCC CP/M kits, a Z180 with 512KB, and a switchable ROM monitor or BIOS running CP/M or BASIC. On to that I've added a compact flash card, a VGA/keyboard interface, and am adding a backplane extender[1] and some digital and analogue I/O.
That provides a solid state, low power system capable of booting into various CP/M type systems and other associated Z80 based OSes.
If you go RC2014 the world is your oyster. It's basically cards on top of a backplane. There's a number of Z80 options, but also 6502 etc. Then you can add video of your choice - simply a serial output, a VGA text out, or i.e. a TMS9918A board switchable to the port locations of various old 8 bit micro locations. So, it's possible to e.g. construct an MSX from a series of plug in ports.
It's probably not the best option if you're explicitly looking to build a specific 8 bit micro (there are other replica systems which handle that better, and the stability of the 80 pin and in particular the 40 pin connectors are sometimes worse than old edge connectors of yore, although probably not the ZX81..)
[1] I would recommend one of these from the start if you're using a kit with only a couple of sockets, two is not really enough. Also, if you use the SC715/SC729 it may need a 5V connector, and it'll be easier to use a backplane with a 5V connector than find one on the main board. Ask me how I know..