If you want TP as early as possible, it'll have to be a sorc - either blizz or lightning/CL, cheap as well with VoR and Crescent moon but squishy.... and no UT and Col. Ancients.
If you can live without TP but still good mobility and do anything with budget, its Warlock (except Col. Ancients) or a FOHdin+Smite hybrid (pretty much do everything with budget gear). ES Warlock with budget gear that do everything is pretty much gone with nerf. Kick+light sin is also up there with budget gear but also excludes Col. Ancients (can do Uber Trist).
Warlock is probably safest for HC general farming given a number of his safety skills (demons, blood oath, psychic ward, etc.) with budget but less so for Uber trist than FOHdin+Smiter hybrid who has definitely better safety with Uber trist and Col. Ancients.
If Uber trist and Col. Ancients is not a priorty, I'd go with Warlock.