Well, I just do it carefully, by hand. A sharp eyeball, lots of tweaks with the hands, and a flat surface helps too. And patience. Same for coils, you get nice clean helices when starting with straight tube with even hardness (if it's been bent and straightened too much, those spots will be work hardened more) and consistent winding.
Coils can be adjusted after the fact, but you aren't going to fix short flats or bends once everything's wound up. To put it another way, there's a characteristic curvature that any turn-to-turn bending is going to favor, and you can't effectively correct features that are higher frequency (having more curvature error over a shorter length).
Annealing can be a mixed bag. It relieves stress, it softens the metal, it's easier to bend. Especially, it's easier to bend out those short, tight curves. But it also collapses that much faster, it's extremely prone to kinking. Use a filler, if you can: Cerro alloys are low melting, good for this sort of thing and reusable of course; it may even suffice to fill with wax (over a long enough length that it doesn't squidge out?), or maybe ice, or sand (remember to pack the sand, and still there's a lot of free space between grains so it's not the greatest).
As for a straightener, if you don't have a proper one, or bearings to make one, it's probably alright to do the same thing out of, like, wood blocks waxed up. It'll take a lot more pulling force of course. Use a clamp, maybe with shims, to set the gap spacing, and go slowly so you take out just a little bend at a time. Make a few passes at different rotations until it's smooth, then step down and so on.
Or for straighter materials, as mentioned, brass tubing can be handy. As kind of mentioned but maybe not made clear: copper tubing comes in different thicknesses. The thin stuff is rigid, not meant for bending -- it will kink too easily. Thick stuff is usually sold in coils and is bendable. There's actually three or four grades of thickness but you'll most likely see just the two at the hardware store. Rigid is more properly copper pipe, and being pipe, its size is coded, only coincidental to its actual dimensions -- as it happens, copper pipe is about 1/8" larger than its code... and that's I.D., I believe? (Tubing is O.D..) Or 1/4" oversize in larger sizes I think. Or in metric countries, it's...whatever it is, you'll have to look it up. As always with pipe, if you need to know -- look it up!
And aluminum pipe, often extruded, is cheap and plentiful, quite straight, and quite rigid and light for its size. You'll need to make good joints (RF connections), which can make the anodizing an issue, but it's usually not a big deal. Yagi, log periodic, dipoles, arrays, all good choices. Should be bendable too, at least over large radii, and given a jig -- would be great for a large loop where the bending radius is acceptable. (The anodizing might even survive the process?)
Steel is fine too, anywhere you don't need large element currents -- not so much for loops, then, as dipoles and arrays. Galvanized steel weathers very well, and can be bolted, compression fit, flared, swaged, soldered, brazed and welded (but do take care to remove galvanizing before welding the area, and clean and protect the joint with appropriate coatings).
Tim