A roof setup can easily withstand 40 mph winds. You just have to make sure to secure it properly. If there was a previous DirecTV/Dish Network setup, sometimes you can re-use their pole mount and coaxial cable runs. If not, you can choose between strapping to the chimney, or mounting it on top of the roof (either screwing it into the roof itself, or using a heavy non-penetrating mount that's weighed down with heavy bricks). Whichever method you choose, make sure to electrically ground your mast (antenna pole) and the coaxial cable just before it enters your house (grounding instructions are at the bottom).

Chimney

Chimney is probably the easiest, as long as it offers you a high-up, clear view to the south.

Here are the poles (the 'mast') onto which you attach the antenna.

Here are the straps that hold the mast (pole) in place against your chimney.

I would buy two of them (they interconnect) for a total of 10 feet, so that your antenna is above the chimney. (You don't want the chimney reflecting signal onto the antenna or blocking reception, even from the 'backside' of the antenna.) Make sure the masts are 'swedged' so they interconnect nicely and stay in place.

If you want, you could also go to Home Depot or Lowe's and buy 1.25" outer diameter EMT (electric metallic tube conduit) that they'll cut for you there. You'll probably need a long truck to carry it home in one piece.

Roof mount

For penetrating roof mount: Use a tripod mount. Pick up some pitch pads and roof sealant also to protect your roof and look at YouTube videos of how it's done. Purchase a pole as described above.

For non-penetrating roof mount (NPRM): choices include the Easy Up EZ NP-60-125 for flat roofs [$65], or for hinged/angled roofs try the AI Satellite NPR-PEK custom-made with a 1.25" mast [~$125 by phone]. Some NPRMs, like the NPR-PEK, already include the pole, so you don't need to purchase separately. Some don't. Buy some thin, flat bricks from a local brickyard (maybe in the same color as your roof) to weigh down the NPRM.

Electrical grounding for chimney or roof

Make sure to electrically ground your antenna mast to reduce the chance of a lightning strike and to minimize damage from one. You use a ground clamp on the bottom of the mast and run 10 AWG copper (Home Depot, Lowes, or online) from the clamp to your electrical service panel (the big circuit breaker box on the outside of your house). Attach the wire to your service panel with a corner ground clamp or side ground clamp. (Look for where any previous DirecTV/Dish installer grounded the coaxial grounding block if you want a hint on where to ground it.) (Yes, two separate things have to be grounded -- the antenna mast and the coaxial before it enters the house.)

For more info about grounding, see article 810 of the National Electric Code, which is adopted by most states.

If there was no previous DirecTV/Dish setup, and you're using your own coaxial cable from the antenna to the inside of the house, then make sure to use an electrical grounding block on the coaxial cable, just before it enters the house. People like the TII-212, which is also a lightning protector.

If you're using the coaxial from previous DirecTV/Dish setup, double-check that their installed ground block on the coaxial line is properly grounded (sometimes they mess up). It should have a copper ground wire that runs to your electric service panel or metal pipe, etc. If not, then you'll need to ground the block yourself in roughly the same way.