While aspirin can be given over a lot longer period than Bute, at least my vet does not recommend doing that without a periodic blood test and does not recommend it for long term such as you are considering.
Glucosamine is ok for on-going issues but if the horse is insulin resistant or cushings, it cannot have glucosamine. It can have Chondroitin/MSM and HA (hyalouronic acid).
My 23 yr old IR horse has hock and ankle arthritis. He's been on chondroitin/msm for three years without issues. The vet said it would be ok to add HA to the mix so I that recently. It has made an even bigger difference in how he comes out of his stall in the morning.
Whereever you buy from just be sure the product is pharmaceutical grade. It will be pricey but you won't use as much.
Aspirin actually comes with the same risk of GI upset as Bute and produces less anti-inflammatory effect. It should not be used daily without taking precautions and you need to understand that it will slow blood clotting in the case of an accident. The best way to use anti-inflammatories is to use as little as necessary to get the desired effect. This may mean dosing every other day at the lowest dose or even dosing only when you know your horse is going to be doing something that generally leads to pain/stiffness. Always discuss medication options with your veterinarian.
Glucosamine can help to reduce pain associated with arthritis. Be sure to choose a product with a high concentration and preferrably in conjunction with chondroitin sulfate.
Many times dealing with arthritis is done by using multiple options---supplements daily, anti-inflammatories as needed, IM products like Adequan, or even joint injections all as an overall program.