IMHO shoot whatever style of bow appeals to you. Bow choice is a personal thing and aesthetics are important - if it doesn't look or feel right to you then you will not enjoy using it. If you want to do the trad thing then go ahead and shoot a longbow or a horsebow as you are doing archery for your own satisfaction.
The principles of good form apply to any bow although some aspects of target shooting form (under the chin anchor, straight bow arms and vertical stance and bow positions) are not always the best approach for some trad styles. With traditional bows I honestly believe you get what you pay for and good bows don't come cheap so if that's what you wish to pursue I wouldn't be spending money on a training recurve and matching arrows unless you're minted of course. Surely your club has cheap training bows you can use until your course ends? Do your homework before buying any tradbow and get one that is made for you after discussing your needs with a good bowyer. Same with horsebows - the sub £200 bows I have tried including Grozers and Kassais are nothing more than fibreglass wrapped in leather and their performance was pretty poor. There are some specialist horsebow sellers but be prepared to spend serious cash if you want to do it properly (I'm not even including the price of a horse
) Good luck with it.