Sure you should get yourself at least an original console of each but if you truly want the best way to play everything Sega without spending thousands of dollars, you can do the following:
• Buy Analogue Mega SG and pair it with a TerraOnion MegaSD (plus Analogue adapter set)
- Plays Sega Card, Master System, Genesis, and Sega CD games
• Buy Sega Saturn with a Retrotink RAD2X cable (for RGB to HDMI) and pair it with a TerraOnion MODE
• Buy Sega Dreamcast with the DCDigital mod (for crispy HDMI output) and pair it with a TerraOnion MODE
This gives you the entire Sega library available at your fingertips all on fPGA hardware (so no software emulation) and you can play to your heart's content. Of course this doesn't preclude you from buying the actual games. If there are certain games you want to start with, you totally can!
As for some of the other ideas mentioned above, the Sega Genesis mini is pretty nicely well made considering it's development is by M2; they're masters so you can't go wrong there. It's a great collector's piece. The ATGames systems previously are total junk. Not even worth buying to include in a collection.
Eva01