Minimum requirements:
1.Decent saddle and pad. I buy used cordura Big Horns on ebay and my ponies love them (all 19 from narrow high withered to tanks) and they have stood up very well. I tried other cordura saddles and they were the pits.
2. Decent bit/bosal: The bit is much more important than the bridle itself so spend your money on a good bit. If you go synthetic get nylon not poly. Bio-thane is really nice if you can afford it.
FYI Nylon and Polyester are much more sun resistant than polyethylene or polypropylene (I used to do the lab testing)
http://www.bioplastics.us/fabricated-goods/cutting-punching-for-webbing-products.html
3. grooming kit.
Hoof pick
soft face brush
harder body brush
rubber curry comb
combo sweat scraper shedding blade.
4. Halter and lead shank/rope (spares are nice)
5. Horse first aid kit ~ Talk to your vet. A pair of blunted bandage scissors are nice for clipping the bridle path.
In the nice to have category:
Mecate Reins: Demo of their use ~ http://www.youtube.com/watch?v=AoKpIIvJnvw
Cooling sheet ~ depends on whether you will be riding your horse into a sweat in the winter.
Saddlebags
Portable fence charger, step in fence posts and electric tape. If you trailer to do camping with your horse this lets you set up a pen for him. It also lets you selectively graze your horse so you can mange your pastures.
For a casual trail rider you do not need to clip your horse or blanket. Therefore a blanket is "nice" to have but not an absolute necessity. Just make sure your horse is walked completely cool and dry. That is what the cooler sheet is for.
I suggest you read up on worming, nutrition and pasture management. A 14 you are old enough to read the information, look at the research and make informed decisions for your horse. I have met several 12 yr olds who are so knowledgeable about horses I thought I was talking to an adult.
NUTRITION:
http://www.applesnoats.com/alfalfa.pdf
http://pubs.cas.psu.edu/freepubs/pdfs/uc099.pdf
PASTURE:
http://www.uvm.edu/~pasture/Documents/Successful%20Horse%20GrazingGH.pdf
http://learningstore.uwex.edu/assets/pdfs/A3529.pdf
Add http:// in front of each link below. Yahoo does not like a lot of links but as a new horse owner the more info the better.
WORMING:
http://www.parksidevets.com/equine/worming.php
http://www.applesnoats.com/strongyles.pdf
http://www.ed.ac.uk/polopoly_fs/1.22255!fileManager/wormingyourhorse.pdf
http://heartland.ponyclub.org/internal_parasite_life_cycle.pdf
Goats and sheep use the same wormer as horses (safeguard, Ivermectin, Quest)
so we can learn a lot from research on them:
www.sheep101.info/201/parasite.html
www.lsuagcenter.com/en/crops_livestock/livestock/sheep_goats/Parasite+Control+in+Sheep+and+Goats.htm
www.tennesseemeatgoats.com/articles2/stomachwormsLice.html
www.jackmauldin.com/manage_your_pasture_better.htm
www.midamericaagresearch.net/documents/Strategic%20Deworming%20for%20Small%20Ruminants.pdf
Article on the growth of a horse:
www.equinestudies.org/ranger_2008/ranger_piece_2008_pdf1.pdf
Apples & Oats seems to have some really good articles I put pointers to two of them above: www.applesnoats.com/olddefault.html and so does shady-acres: shady-acres.com/susan/index.shtml