>>>What does the word "base" refer to in some of the ebay cars.
Not sure, as these cars really didn't have trim levels like American cars did at the same time. An MGB was pretty much an MGB, just had a small handful of options. Triumphs were pretty much the same.
>>>Is the mgb gt more desirable than the convertible?
If you go by the pricing guides, no. Convertibles (of almost any marque) are usually more valuable as, well, the top goes down. Often seen as a big plus in a fun car. That said, the MGB GT is a really nice looking car and would have some advantages in cooler weather. The biggest difference is that the windshield in the GT is a couple inches taller -- so that you've got a bit better visibility when the top is up. That said, I'm really happy with my MGB tourer, the top works well (at least to keep warm) and it is nice to be able to go top-down.
>>>What is the comfortable cruising speed of these little cars?
My stock MGB with factory overdrive can easily cruise at 70mph all day (I've done it). I've no issues with freeway driving -- the overdrive makes a big difference here.
>>>And finally, are there any big advantages of the triumph or mb over the other?
They're both great marques. I've had both, and there are plusses and minuses to each. I'm a reasonably big guy (6'1", 210#, big feet) and I find the MGB roomier than the Triumphs (talking TR3 and TR4 here). They made 500,000 MGBs, so they also tend to be cheaper to buy. Running costs and parts availability is similar, though the MGB is probably one of the best supplied classic cars in existence.
Triumph engines, if all stock, tend to be a bit more powerful. Both can be modified for more power with plentiful options.
To sum up, it's pretty much down to what makes you happy. Can't go wrong either way. Find the one that draws you in and go. These are simple and robust little cars, some of the best fun-to-cost values in the classic car hobby.