+1 to a french press. They're fairly cheap, easy to use, hard to screw up with, there are no consumables, and they are generally easy to keep clean. If you use a blade grinder, you will get plenty of sediment, though. With a burr grinder, the amount of sediment will be fairly small, just a few times more than you'd get with espresso.
Note that Bodum has started slacking on quality, in the face of cheaper competition. A bought a new one a few years ago to have one at work, and it did not impress. If you check out reviews, notice how so many of the bad ones are having issues well after purchase.
My more recent one is hard to clean the silt from the plastic grate, the plastic top section does not fit straight on the beaker (IoW, coffee cools down quicker until it is no longer steaming), and the band holding on the handle is already rusting. My nearly 15-year-old Bodum press, meanwhile, has no corrosion, perfect-fitting parts, and the plastic is all easy to clean (hot soapy water soak for 5-10 min, worst-case, will get it odor-free). That the nut was plastic, and eventually stripped, is the only con I can think of to it (I now use my old press, with the nut from the new press

).
Classic bean-counters-riding-a-brand-into-the-ground story, I'm sure. Today, I would either get a cheaper one, or a more costly brand that prides themselves on quality.
Lately, I've been really considering buying a coffee roaster. My Cousin has friends that run a green coffee reseller business and NOTHING tastes better than a cup of coffee brewed from freshly roasted beans. My lazyness has been the only thing stopping me. Home roasters tend to only handle small batches, and It does add a significant amount of time and effort to get that first cup of coffee.
An air popcorn popper with vents on the sides of the cylinder, rather than the screen on the bottom, is cheap, and fairly easy. A metal colander with large circle openings (as opposed to thin slits) can get rid of most of the leftover chaff, and helps cool the coffee down. You won't get the consistency of a machine made for coffee roasting, but you will get good coffee, with a bit of practice.
I've not needed to bother with one-way-valve bags or any of that, just a jar with a tight-fitting lid, after it is a couple days old. I figure if it isn't used up in a week and half, I've made too much.
On espresso machines, the key reason to avoid the cheap ones is cleaning. I had one, and it actually could make a decent cup...for about the first 3 months. If you can't take it apart in a matter of minutes, to clean every single surface, consider it garbage (good espresso machines will also have materials safer for running acid/base cleaners through them, where most dept store ones have a fair bit of bare aluminum).