Are you asking for how the procedures work, or for someone we may be able to recommend you to? I can't speak to the latter but can explain both processes, which you may want to use both to get hair down.
Electrolysis is taking a pair of tweazers which send a signal through the hair(there are multiple versions of signal and method but all of them basically do the same thing) which kills the pholicle. This is a very long process, and is somewhat painful, as the technician performing the technique will need to do each hair, and basically amounts to them aggitating the pholicle while also forcibly removing the hair from the root. I don't really recommend electrolysis for large hair removal, but it's an invaluable technique for spot removal of stubborn hair that won't remove itself after other methods.
Laser hair removal comes with pain too, but I've found it minor in comparison. Laser Hair removal is great for large areas of hair, but falters in spot removal and can leave some thick hair behind even after the full process. If you are trying to generally remove a large amount of hair from a location, then laser is best for that. Laser hair removal works by firing a light laser over your skin, this laser is made to burn out the hair through it's pigmentation, leaving your skin unburnt, but burning the hair pholicle so that it becomes damaged and unable to regrow.
In both cases, 1 or 2 treatments will not have much noticeable effect because hair grows in waves. Underneath your currently growing hair is another wave of hair that will grow on a different cycle. The only way to get rid of such hair is to have the process done at set intervals(usually about a month) over an extended period of time. In both practices, as I've seen, you can also pay less by paying for all treatments up front, but different pay plans exist based on the location and process you choose. I'd recommend starting with laser hair removal to get the majority of it handled, and then, if you find hair that bugs you but is isolated or just didn't manage t get handled by laser removal, do electrolysis.