WARNING: Useless pieces of advice to start with: I've had some end grain cutting boards that required a lot of smoothing. An 1/8" is a LOT with end grain. I've found it really helps to fine tune the fence/ saw/ sled you're using, to keep the variance to a minimum when you make the second set of cuts. A gram of prevention is a kilogram of cure (this expression doesn't really convert well to metric....)
A 5" random orbit sander can take a long time, even with 60 grit. I recently purchased a 6" sander and that helps quite a bit. I also have a drum sander (Performax 16/32), but it's no panacea. With end grain, it's easy for a piece of grit to get 'stuck' and then you have a scratch across the length of the board, which then needs to be sanded out. It is also really easy to burn the board, which means you have more sanding to do in order to get rid of the burn marks.
A wide belt sander is the way to go. In the time it takes you to say "wow, that's a big machine" the boards are sanded. And you better talk fast.
I've also successfully used my planer a couple of times. The opinions on the safety of this approach vary. You definitely want to first round over the edges (like Sam suggested), and then take VERY light passes. I should point out that I have a planer with helical head, and those carbide cutters do really well on end grain. A planer with regular knives may also work, but there have been reports of people shattering the board and/ or knives.
A third option which isn't too expensive is to make a router sled and level the board using a straight bit. The
Wood Whisperer has a video on flattering a bench top, this is pretty similar.
As for which woods to use, you want something with a tight grain, that's not porous. Walnut, maple, cherry, purpleheart and white oak are good choices. Red oak is not.