A MUST is gas-flowing the cylinder head. That is the key to improving performance. Valve sizes should be 35.6 mm inlets and 29.5 mm exhausts as on the MG Metro and the 1275 Cooper.
The EVO001 cam will then work well, but do ensure that it is accurately timed in either with vernier duplex sprocket or by using offset woodruff key sized to suit after measuring.
Personally I would go for an HIF44 carburettor on a cleaned up inlet alloy manifold. Exhaust manifold needs to be a 3-into-2 'Freeflow type.
The final drive ratio is far to high at 2.76:1 and I would recommend either a 3.2:1 or, for best acceleration, a 3.44:1 which was the standard for the original 1275 Cooper 'S'.
With the compression ratio set to around 10:1 that should give you 75 to 80 bhp, but with the more important good torque between around 3000 and 5700 rpm.
Whilst it is in pieces you would be wise to rebuild the diff itself as diff pins are high-wear items. A lot of us fit the cross-pin diff as it lasts a long time.
To get best performance, the quality of the build is very important with all calculations and machining done accurately.