Hey Gamefan, we've been there before, eh.
The initial cost of either a reasonable MISTer setup or original hardware + SD/ODE will be quite considerable which also depends on the monitors or TVs you are going to play the games on.
MISTer outputs HDMI as a standard so you can connect it to a current TV straight away. Original consoles usually have RF, Composite or RGB output so you would need an upscaler like OSSC or Retrotink to get a decent picture. Of course you could also go the oldschool route and get yourself a CRT TV for the old machines. However, you might have to mod some of them to improve the video quality which would add to the overall cost.
There are SD carts (Everdrive) for cart-based systems and ODEs (optical disc emulators) for disc-based consoles like PSX or DC, both let you use ROMs/ISOs to play on the real machine. Everdrives are easy to use, just put some ROMs on the SD card that comes with it, put it in and you're set while ODEs need a bit more effort to get it to work. Some of them completely replace the old optical disc drive of a console, others are an add-on that still lets you use original media on the system. This may be something to consider if you still have some original games which you want to use on the real hardware.
There still is good old emulation, tho - all you need to get access to tens of thousands of games is a moderately fast computer, a few emulators, ROMs and maybe a USB pad or stick. Emus like MAME have come along way and even if there are some games that still aren't 100% emulated, the vast majority of them run flawlessly. It's by far the cheapest way to play older games, including those on disc-based systems like PSX or DC.