If you just want to play with logic, you can look at some simulation software. Titles I have used are logicly and logisim.
Logicly also has a web based version (at logic.ly) so you can try it out before you might decide to buy a copy. You can also build up your own modules to include into future circuits which I found was quite valuable because you can build up familiar 74 series logic chips to make circuits that are more like what you can build on the real world.
Logisim seems more limited in that respect, but has a lot of other things that logicly doesn't, like ROM/RAM simulators.
I've used both for proofing some of my own designs before committing to a bunch of soldering or ordering PCBs.
Personally I've found it easier to whip something up in software like this and make changes with a few mouse clicks than having to deal with the tediousness of a breadboard, and once I have something that works the way I need I look at designing it into my project.