For filters, the Aquaclear line are really good for Bettas since they have adjustable current, so that you can make sure the flow isn't too strong for him. The Aquaclear 5-20 gallon filter works perfectly. I also like the Hagen Marina Slim filter line (e.g. the Hagen Marina Slim S10), it also has adjustable current. If you are getting shrimp too you might want the Marina one, since it has the intake covered. Very young shrimp can be sucked into filters that have an uncovered intake. Be aware that some Bettas will eat Ghost Shrimp, though.
There are lots and lots of good heaters on the market. The best ones have 2 features: 1) dials where you can adjust the temperature exactly and 2) automatic shutoff, so if the water gets too low the heater will simply stop working rather than cracking and electrocuting all the inhabitants.
For decorations, I've found that Bettas particularly appreciate two things. The first is floating plants. Any type will do, they love hiding around them and building bubble nests using them. I have live plants for mine. Amazon Frogbit and Dwarf Water Lettuce are my floating plants, they both have trailing roots that go into the water that my Betta loves to twine in and out of. Of the two, Amazon Frogbit is easier to grow. Salvinia, Hornwort, and Lotus are other floating plants that don't have roots but that are still great for cover and bubblenests. If you don't have live plants, I recommend silk. Some plastic plants can tear a Betta's fins. You can tell if they are Betta-safe by seeing if they tear pantyhose when it is run against it, if it doesn't tear the hose it won't tear fins.
Bettas also really like caves with large openings that are hollow inside. They appreciate having a dark, private place to go to.
Shrimp appreciate any type of moss. Tie it to a decoration or piece of driftwood for it to attach to with cotton thread.
Bettas do not like bright lighting at all. I've had one of mine turn to tail biting because bright lights stress him so much. So don't get really fancy plant lights that have more than 2 watts per gallon, and stay away from the bright new T-5 lights, that put out a lot more light per watt than the T-8s do. Floating plants can be used to dim an aquarium, too. I've also noticed they react badly to very unnatural color temperatures, so try to keep towards a daylight spectrum.
Bettas are also jumpers, so make sure there are no gaps in the hood. Leave a couple inches of air between the water level and the top of the aquarium. Bettas can breathe atmospheric air (with their labyrinth organ), so make sure they have access to it. They will drown without atmospheric air. They also do better if the air is warm and humid, so closing up any gaps in the hood with plastic rather than mesh is benefiical. I like the tops that are glass with plastic fitting on them to cover gaps, and then I put a light on top of that so they have the most humid air possible, which is good for their labyrinth organ, rather than putting on just standard hoods.
For foods, New Life Spectrum Betta Formula and Omega One Betta Buffet are really good foods. The more variety you have, the better. Its also beneficial to give him treats of frozen aquatic insects, such as blood worms or brine shrimp, a couple of times a week. You can get these at most pet stores. Thaw first, of course. You want to stay away from freeze dried foods with Bettas, since they are prone to constipation. For dried foods, always get Betta food, which have the high protein percentage Bettas need.
For tank size, try and get at least 5 gallons. 5 gallons will work, but 10 gallons is absolutely wonderful for them, like a palace. If you decide to divide a tank, make sure each Betta has at least 5 gallons to himself and be sure that they can't see through the divider. Fish tank mates are hit and miss, and a Betta is not any happier with tank mates than he is alone.
Also make sure that you do a fishless cycle before getting the fish and that you do weekly partial water changes (25% should work well) after getting him. For dechlorinator, I really like Prime because it will detoxify any Ammonia, Nitrites, or Nitrates that may be in your source water, although you will still need to cycle the tank of course.