Turbo's are great but come with a few complications in mini - namely space but then cooling, space, clutch life expetency (unless you want a grabby race spec item), space and lastly gearbox/diff reliability. Obviously all these things can be overcome if you want to throw enough money at it but it is not simple or cheap. There also isnt really a one stop kit to fit to a mini so alot of stuff needs to be made or fabricated (unless you find an MG metro turbo lump complete but even then stuff still needs to be made to fit)
I went 1380 as it is well proven and reliable and there are plenty of options piston/parts wise. What I will say is I ended up spending far more than I initially thought. Some of this was down to spec upgrades (didnt see the point in spending 60% of the cost of new stuff to remanufacture old) and some of this was down to faults that I didnt know about and subsequently found with the block and gearbox.
As per the other posts above the actual spec of your engine will very much depend on your budget. Im sure there are a million and one variations on the best "road spec" engine but I would say get a decent road spec head from a reputable seller (some links below) a decent Cam (Swiftune SW5 seems to be the road spec cam of the moment) refurbish your gearbox and fit a cross pin diff for reliability (also worth looking into final drives as this can make or break a road car)
Also not knowing the condition of the rest of the car its worth remembering cooling as most minis were already on the limit so all new parts for the cooling system and upgraded rad are a must with any engine upgrade. Also brakes and suspension as if these parts arent in good condition theres no point in adding more power.
Keith Calver is a bit of mini legend and writes technical artricles for the mini mags and races his own car. Its worthwhile having a look through and reading the technical articles on his website he also sells pistons (believe of his own spec) heads and some other parts but definitely worth checking out:
https://www.calverst.com/
MED are for all things A series. Everything I have purchased from them has been top quality they also have a load of technical vids on youtube that are worth a watch:
https://www.med-engineering.co.uk/