Depending on what you’re carrying, you may not even need a rack. A company called Kanga makes a line of rooftop “pouches” that are heavy waterproof bags. These attach directly to the roof, hooking either to the door tops or to a factory luggage rack. They work great, and are not that expensive. The ten-cubic-foot Typhoon model, for instance, goes for about $150. An optional pad to give your paint a little more protection is $10.
Other than that, all the major brand-name racks made are really, really good. I use Yakima stuff, but that’s not necessarily an endorsement as the one to get. I will say this: Yakima’s Loadwarrior basket ($275) is an incredibly useful attachment. I was able to stick mine right onto the factory rack on my Subaru Outback. But it also fits to any Yakima or other maker crossbar set. Bike racks or other accessories attach right to the Loadwarrior, leaving plenty of room for duffel bags or other gear. On a car like the Civic, you’d be creating an enormous amount of very flexible hauling space for everything from camping gear to bags of garden mulch. If you wanted to go all-Yakima, then the Q Towers fit your car ($309 for the set, with crossbars).
In Thule’s line, the analogous setup would include the Aero Foot Pack, crossbars and perhaps a short roof adapter kit. About $300. Thule’s Playpen basket ($250) is similar to the Loadwarrior. In Saris, you’d use the 50-inch Load Bar ($219). I haven’t used Saris racks, but their reputation is very good and they have incorporated some “clean sheet” technology whereas Yakima and Thule are a little encumbered by past designs. The Saris racks tighten from one side, for instance.
A Kanga Roofpouch, by the way, ties nicely into any of these after-market racks.