Originally Posted by
A0X0M0X0A
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Shimano Deore 9-Speed Mountain Bicycle Rear Derailleur - RD-M51 $38.53.....
Do you mean M591 ? If so, it is a good RD.
Originally Posted by
A0X0M0X0A
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Shimano M361 Hybrid Crankset (Black) $35.78
Shimano BB-UN26 Square taper Bottom Bracket (68x113-mm) $42.20
The M361 works with a 122.5mm BB axle. Unless your frame is incredibly narrow, the inner cog will rub on your frame.
I'd not know your source for parts, but the pricing is a bit high.
As noted above, you also need a 9 speed cassette, or change the shifters to 8 speed. The shifters and the cassette have to match.