Engine choices...ok, first question is, what do you really want from the engine? I think we can all agree that the standard 1800 B series engine is, and I quote others here, "at best, a boat anchor".
Personally, I think that is a little unfair, and bearing in mind the unit started life in the late 1940s as a 1200cc engine, it did well to achieve what it did as a 95bhp 1800cc unit by the 60s. Sadly, without going into historical detail, it is not the fault of the B that it remained the B series until 1980, despite the best efforts at Abingdon to fit the O series OHC unit.
So what choice do you have to update the MG B? If originality is important then there are a couple of period tuning tricks that will get the engine producing a bit more, but if you are on the slippery slope to all out power then you may as well go straight to V8!
Before rushing off to the scrap yard (or is it eBay these days?) don't forget to read the words of caution here!
I recently tried to create a Decision Matrix to determine the best choice of engine for a conversion and apart from the lower cost of tuning the B series, the V8 came out as probably the easiest conversion. The matrix took into consideration the issues relating to the cost of engine, cost of conversion, cost of insurance, impact on resale etc etc, so it's no surprise that the V8 wins - nothing comes close to the torque or the aural pleasure it offers. But it's not a Sunday afternoon swap. And if you are blessed with a later rubber bumper B your life will be easier, but fitting badges and V8 wheels will be the easy part!
However, the V8 will get no further mention on here as it is very well documented elsewhere, and frankly, in the humble opinion of the site authors, is too common for inclusion! We aim to be different here!
So, it comes down to a matter of personal taste, your budget, and what you happen to have lying around in the back garden in the way of a donor! There are any number of possibilities for the MG B, but it comes down to cost inevitably.
The
B is quite upgradeable within a reasonable budget and offers the advantage of being useable for historic car racing/rallying
where originality is concerned. 1860cc, stage 2 head, cams etc. So this must be
the benchmark against which we examine the other options. Bear in mind that the
distinct disadvantage is the the engine is somewhat obese at >200kgs fully
dressed. But, an "easy weekend project" nevertheless with tried and tested upgrades
taking it to a respectable 30% power increase if done right.
The supercharger option immediately adds to the cost, but again, a straight up 40%
improvement on the standard engine with minimal plumbing and no wiring hassles.
And a massive rarity factor, although now Moss are offering a kit, it is
becoming more popular.
Before you go any further, there is another word of advice here, and that is to assess both how well your car will handle the extra power, and whether is it up to stopping the car from the greater speeds it will most certainly achieve! Braking and suspension must be factored into any conversion programme, preferably before the engine upgrades.

Of course the obvious other candidates are Rover's perfectly brilliant T16 and K16 engines, the former being the easiest and in hindsight, would be the best option in terms of cheapest potential upgrade for power. Read why Chris Hassall likes it so much and sees a family link in this process.

Some people will go straight for the V8 option, but for others there exists a whole choice of engines worth considering. But before you go down that route, is the B Series an option? You decide.