I want to run just 2 characters. Both hobbits. With my main as a minstrel/yeoman I want to make an alt that also wears light/medium armor, that can help by preparing hides for the tailor. Would I be right thinking hunter/explorer is the best option for this? If so would it be an option to ignore the prospecting side and only collect wood, animal remains, foods?
Warden, hunter and burglar all wear medium armor, with warden and hunter being a bit better than burglar IMO (porting and run speed toggles). Problem with being explorer is they are also tailoring anyway. No need for your yeoman to do it. and it is MUCH easier to have your crafter capable of making the components and gathering the resources they need. (trust me, I tried weaponcrafting with my scholar. Not a good experience)
You can ignore the prospecting side, but I would highly advice NOT doing so. There is much gold to be made in gathering metals and selling on the auction house. ( yes, You're F2P, and can't sell on the auction house. Use the TP, buy the slots, or buy some TP with cash, or pay for one month, whatever, but gain access to selling on the AH). I would recommend using TP to remove the gold limit as well, if you haven't already.
I agree with Khorgrim: you can earn quite a bit of money by prospecting ore and selling it, or processing it first THEN selling it.
I also think you will find yourself much less frustrated (less sending crafting materials back and forth between characters) if you just use your yeoman for food and your explorer for armour. If, however, you decide you really want your yeoman to do your tailoring, you could choose woodsman. This would give you forestry for the hides/leather, and you could make bows for yourself. You would probably have more monetary difficulties since you wouldn't have quite as many valuable extra materials.
I also agree with the opinions above - it's far better to pick an Explorer as your other character's vocation, as it gives a lot of opportunities and is a good source of gold, which you will need to progress faster with your cook. Not to mention that if you by any chance decide to start another character and another profession, it will be much easier to be supported by a high-level explorer.