>>1912934rear cassette:
you have 8 speed Shimano freehub on your wheel and Shimano mtb rear derailleur.
any Shimano or Shimano -compatible 8 speed cassette will work, including road cassettes, but you probably will want one the exact spec to that you are used to riding, unless you don't like what you have and specifically want to change it. so, you need to figure out what the tooth count is on the biggest and smallest cog. it should be stamped into the metal but you can always just count. you don't need to know the tooth count of the ones in between. then you can match or adjust as needed. there may be different options with the same spec, the prices will vary based on weight and like off brand stuff may be cheaper but they'll all work
front chainrings:
these bolt onto your crankarm separately from each other and usually the middle one wears out faster. you only have to replace the worn-out one(s).
however , different crank arms are different sizes and the bolt paterns are different. lots of mtb use 4 bolts, but it could be 5, so that's the first thing you have to match. then the size is specified in terms of how far apart the bolts are from each other: the bolt circle diameter or bcd. this must match exactly but beyond that you can buy steel, alu, cheap, expensive, whatever.
again, you probably want the same tooth count that you're used to but if you need higher or lower gearing you can get more or less teeth within your bcd, but bcd sets a hard limit on the smallest tooth count that will fit and usually that's the stock size, so lower may not be an option without changing the crank.
bcd should be stamped into the crank arm somewhere and tooth count will be on the rings, or count them
