Lots of adults with ADHD choose not to take meds, and there are both the stimulants like ritalin and adderall that everyone knows about and non-stimulants like Intuniv or clonadine, so there isn't an easy answer to any of this, it's just what works or doesn't work for you. I agree with what others have said, finding a specialist rather than just your GP would be best if you want to pursue meds.
One thing that I think is not commonly known about ADHD is that a huge component is also emotional dysregulation. We go from 0 - 60 instantly and it's hard for us to calm down, sometimes impossible. The "hyperactive" in ADHD doesn't just mean physically, because a lot of us are not actually physically hyperactive. But we are emotionally hyperactive. The ADHD stimulants calm that down for most people. So if you found an ADHD med that worked for you, it's possible you wouldn't need the other med. But again, since this is so subjective, that's only a possibility.
All ADHD meds help with focus, memory, patience, and as I said that calming-down of the emotions. Where I used to panic when presented with even minor problems, now I have the ability to take a deep breath and think through them. I'm also happier, where antidepressants never worked for me, because the stimulants are a big hit of dopamine right to your brain. But individual responses to them are so different that you'd have to try for yourself, and like all psych meds you just won't know unless you do. The nice thing is that they are very quick acting. Unlike your antidepressant, you'll see a difference within a day or two, probably within an hour, after taking it. You don't have to wait six weeks to know whether it will work.
You can google the side effects for yourself, but the most common are tension headaches, not being hungry, and insomnia, though for other people they can actually help with sleep. A good specialist should let you do a trial and let you stop pretty quickly if you don't like how they make you feel. Good luck!