We have one of those 900 gallon.. 2.5' deep by 16' wide semi
inflatable swimming pools, with an water filter running (8.5 hours a
day after 7pm)...

I'm having trouble figuring out the proper chemicals i should be
buying.. and what that cost probably is per season.

At this point i've bought the shock granuals that come in a bag for $3
and should be applied weekly. The directions call for an entire bag
per 11,000 gallons.. Our pool isnt filled to capacity due to slope..
so say it has 650 gallons.. i guess this would imply that each week i
should be putting in about 5.9% of the bags contents.. whatever that
is in OZ (probably 5.9 of 16 oz) and then teaspoons i guess?

Also.. the bag mentions following the 4 step guide..

water balancing, chlorinating (or bromine), shock treatments, and then
algae treatments..

Other than this shock treatment.. are the other 3 done only in the
beginning of the year.. and what does this imply? Do I simply go
stock up on ph balancer (or akalinity), bromine or chlorine, and algae
chemicals, then apply these once, followed by weekly shock treatments?

At any rate.. so far I've only used the shock treatments.. i had gone
like 3 weeks without doing one.. and algae (slimy on the bottom/sides,
slightly green) was appearing.. so I used the underwater sucker device
and strainer to remove all that i could in general.. then applied the
shock.. but even after 20 minutes the water feels very slimy.. i'm
worried i may have a mess that cant be fixed... or perhaps i just need
the other 3 chemicals..

(I guess if i did bromine i could avoid chlorine.. is chlorine linked
to any conditions that should be avoided these days.. seems like you
dont see it much, though the shock treatment says it has 45% chlorine
in it i think.. i thought the shock was all 4 steps but i'm a bit
confused now)..

Thanks for any tips..