I doubt you could get a restored mini for a grand. If you bought just the shell then you would need to source all the other parts as well. You really need hilos or adjustable coil overs to corner weight the vehicle as the new engine will change the weight distribution. The money you have I would expect to spend on the conversion alone. I doubt you would be able to buy a mini with that as well as do the conversion. An All speed frame is £499 plus shipping. Then there is the shafts, lower arms and other bits you will need.
For the exhaust its probably best to get a full stainless system built. You get the added bonus of a life time guarantee. Either that or take the corsa one and modify it to fit. That is one of the many problem areas. Changing the exhaust may loose you power
To get it to fit and working you will have all the following problems to over come:
- Mounting the engine and gearbox
- Sorting out a useable gearbox
- building up drive shafts
- wiring
- controlling the engine from the accelerator pedal
- clutch linkage
- gearshift linkage
- finding a radiator that is big enough to cope but able to fit
- body work modifications
- making the exhaust and inlet manifolds fit
- Fitting an inter cooler somewhere
- exhaust system to build
- possible relocation of the master cylinders
- Alternator fit ment
- A load of other things I have probably missed.
If you have never done an engine swap I would suggest doing a tried and tested one first. A red top conversion will give you 150 bhp. Throttle bodies and aftermarket ECU will give you more.
I had done other engine swaps before I attempted the Vauxhall conversion on my mini. I've not seen an x18xe1 powered mini on the road but the engine isn't too dissimilar to the the x16xe.
You also need to remember that a mini is almost 600 kg lighter than a Corsa VXR. 100 bhp will make a mini shift. You probably won't need 189 bhp like the Corsa VXR has straight away. With that kind of power you will probably need to start looking at upgrading other parts to be able to cope with the power. A mini was only ever really intended for about 65 bhp. There have been models with more but the mini was always intended to just be a normal small family car.