Your speed controller choice would be good.
The motor can be anything you like - a normal 27 turn stock motor will give quite a power boost over the standard 540 - I wouldn't go below about 17 turns with a motor though because the car will probably become uncontrollable.
You can fit 1/10th rally tyres on the car - but they are a bigger diameter than the Mini Tyres, and will probably foul the body. There are a couple of solutions. One is to cut a lot of material away from the wheelarches. Another is to find another body that has flat sides, rather than the flared wheelarches of the mini. I use large diameter tyres with an HPI VW Golf shell. That shell has a wheelbase of 225mm, whereas your mini is 239mm. To fit it you need to buy a "chassis extender" by Rcboyz from ebay.
The car already has plenty of suspension travel - I would not buy longer shock absorbers, as the driveshafts may start binding. When you fit the rally tyres, the ground clearance increases quite a lot anyway. Oil filled shocks, like the CVA units, or the various Tamiya alloy units should make the car handle better.