My advice to any new archer is to firstly be sure of your draw weight and length, the bows that you use for a beginner's course are usually very light in draw weight and you will need to buy equipment which will allow you to shoot the distances you will want to shoot. Having said this, if you are a young archer who is still growing you must be careful not to buy a bow which will cause you damage!
You should also bear in mind that over your fist year, you will more than likely "grow out" of your first bow as your muscles and shooting style develops, for this reason you should not buy the better top class equipment as you will probably be selling it on within the year. Having said that you should buy the best you can afford at the time as some of the cheaper bows can be a bit inconsistent. I would advise that you go for a bow that has ILF limbs as then you can buy a decent riser and just upgrade the Limbs later on!
Bows come in different lengths according to your draw length, your coach or the dealer can advise you on this.
For arrow selection you should start off with aluminium arrows such as the
Easton
Jazz series, they are good quality, reasonably priced all-rounders which you will be able to find with a metal detector if you miss and can be straightened if you bend them!
If shooting recurve, the essentials you will need to buy are a Bow, Arrow rest, Arrows, a sight and a quiver, tab & bracer. Next on the list but not quite so essential (but you will find that you need them very quickly) would be a bowstand, a bowsling, a chestguard and a bag or case to keep it all in.
A kit list for Compound would be much the same but with the substitution of a release aid instead of a fingertab. You will also need a Scope and peep sights. I would not generally advocate going straight on to a compound bow from beginners stage although some people do and succeed! Compound bows tend to be a bit more expensive to get started with and care must be taken to get the draw length right! They are also a bit more technical and at that stage you need to be developing your basic technique rather than concentrating on these other aspects!
When buying a bow, make sure you try it out first, this is essential, each bow is different and one bow of a given poundage can feel entirely different to another of the same weight even with a bow of the same make, so it is important you feel it for yourself and bear in mind that if you are thinking of going on to shoot tournaments, you will be drawing the bow 150 times through the day, so that bow which feels easy when you are fresh in the shop will not feel the same as it will for the last couple of dozen arrows near the end of a shoot!
Before visiting a dealer to buy kit, you should always check at your club as there is often good beginners (and intermediary) kit up for sale there as last years beginners move on, there are often some bargains to be found!
Lastly, visit the links section of this forum, in there you will find a free book that you can download called the Archers Reference which will give you lots of good information, it's well worth a read!
Hope this helps, good shooting!