You'd honestly be surprised -- losing weight can make a big difference on fat below the chin. If you're looking for a more dramatic improvement though, your best options would probably be either liposuction or CoolSculpting. Liposuction is obviously a surgical procedure (aka a bit more invasive) but it will permanently remove the fat cells. CoolSculpting is nonsurgical and "freezes away" the fat cells, but it may require a series of treatment sessions over the course of a few months to get the final results you're looking for. Search for "CoolMini" if you'd like to learn more about the specific "under the chin" version of the CoolSculpting procedure.
For the record, the fat reduction injections do work. But from what I've heard from clients, the recovery process makes you look like a bullfrog after and can be fairly uncomfortable.
When it comes to saggy skin along the jaw and neck, a facelift or a neck lift is the best bet! These procedures will tighten the skin, readjust any drooping facial muscles, and help define the jawline. If you'd like a nonsurgical solution, you would probably want to look into laser treatments that utilize radiofrequency (RF) energy. The heat from the laser stimulates collagen production and helps tone the area, but the results won't be as dramatic as a traditional surgical procedure.
As for cost, I'm an American so I only know North American prices. A facelift usually goes for around 10 to 15k. The cost can vary a bit depending on your surgeon's level of experience, etc. But this is definitely a procedure you shouldn't cut corners on! It's worth the investment -- it's your face after all, haha. When it comes to recovery, you can expect to go back to work around 2 to 3 weeks after the procedure. But your results will continue to develop over several months as your skin and muscles settle into place and swelling subsides.