Stuttering on stop, other issues

My main problem is intermittent, but when coming to a stop it stutters through second gear. When in 1st there is no issues, and 3rd/od no real issues. On acceleration it sometimes is sluggish through second gear. If I'm trying to cruise in second it will sometimes shack and buck. I occasionally have a rattling noise, but can't track it down. Other times it growls on the highway, but it is occasionally and doesn't seem to just be in the turns. Any ideas on what to tear apart first?

I forgot to put in that on hard braking there is a loud thudding noise.

Sounds like stuck/dragging brake pads or calipers or a warped rotor to me.

Post your year and engine. Always helpful and will get you more specific and better recommendations.

For the brake symptom, you need a thorough inspection of all brake components. Have you ever repaired/replaced brakes before?

For the "stuttering" symptom, best strategy is to start with simple stuff first. That means tuneup hardware. Plugs, plug wires, distributor cap, rotor. If you have a check engine light or even if you've seen one and don't have one now, read the codes.

For the rattling noise, noises are notoriously difficult for us to help you with. You need to isolate a little more. Sometimes having a buddy can be helpful for this. Is it in the exhaust area? Coming from engine? Rattles can be a loose exhaust component. Again, an inspection is the best way to start. Get it up on a hoist and check everything, paying special attention to the catalytic converter and the heat shield on the cat.