Is it safe to go back to soccer after ACL reconstruction? What type of brace will I need? Would you recommend going back to play soccer and run track?

Yes, In most cases people can return to sports (including soccer & track) following an acl reconstruction, especially if it is the first time you've had a tear. However, return to play comes after months of rehab, and usually includes bracing. Your surgeon can help you decide which brace is best for your specific needs (may be custom fit bracing). For more info:
Yes. The reason you have an acl reconstruction is so you can resume activities at the level that you enjoyed before your injury as well as to avoid or protect your menisci and prevent arthritis. If you have rehabilitated your knee which can take up to 6-12 months and you have the go ahead from your surgeon/pt please go ahead. Surgeon cna recommend a brace they are too numerous to detail.
Ask UR Orthopedist. Only the surgeon who did the reconstruction, or your physical therapist should answer those questions--unless you are trying for a re-reconstruction. If cleared, then should be ok and brace more for psychological support than mechanical, but really need to hear it from your dr/pt.