I am a western and english rider but I may be able to help you out... what are you planning on doing with your horse? Jumping, dressege, trail riding, etc?
You will need:
-saddle, $$ depends on brand and quality 200-1000+
-bit, depending on bit, snaffles are around 25-40,
-saddle pad, 20-40+
-polo wraps, 30
-martingales, standing 50-80, running 50-80
-extra reins, sturrips and sturrip leathers (incase saddle or bridle don't come with them) ranges from 40-60 per set
Starter tack sets are available, but not very good quality if you are looking for cheap. And they may not include everything you need.
For the Horse:
-grooming set and bathing tools, 60+ for a 7 peice set
-shampoos and conditioners, 10-20 per bottle
-halter, 10 for nylon, 10 for rope halter, 40+ for good leather halter
-lead rope, 8-15 per rope
-lunge line and lunge whip, 10-20 each
-first aid kit with vet wraps and stuff, price depends on the whats inside
If you want to go all out:
-sport and splint boots
-minerals for the horse
-pellets or a grain
-beetpulp or something for a filler
-fly masks and fly boots
You may want to get extra halters and leads, incase one breaks or gets lost. There is a lot of stuff you can get for your horse right away, and some you can get with time. (I personally have more then I need, like 20+ halter and leads, 5+ lunge lines, 2+ sets polo's, 6-7 bridles, 2 saddles, etc, and I have only had my 2 horses for a year)
-tack cleaning supplies
-barn hardware (snaps, crossties, etc)
You want to get more then one bucket, especially if you are going to use it for different things, get different sizes too.
Although you said you already have those, you should get an extra of each, I know I broke my helmet at a show from a nasty fall I took, and had to get a new one... and I have 5 pairs of boots (english and western)
I know this is a lot. Not all of it is nessasary, but is good to have. If you are planning on showing, then a lot of this is necessary. I know any chance I get, I buy more horse tack and stuff, I have WAY more then I need, but it is good to have incase I do need it.
Here are some websites that have some fairly cheap items that you need. Horse Tack | Horse Supplies | Horse Accessories - Statelinetack.com Perri's Leather - Quality Equestrian Products :: Leather Halters :: English Tack » Index
Hope this helps.