My experience of Belarussian visa's from a UK perspective in 2010 was:
-We used an agent to help us book a hotel, the hotel booking came with the letter of invitation
-Due to this we were only able to book from a limited pool of hotels in Minsk, at fairly premium prices.
-We were strictly limited to entering on the day we first stayed at the hotel (we had originally intended to visit Brest Fortress during the day and pick up the night train into Minsk, arriving there in the morning, but the embassy wouldn't allow us to do this).
-We were a little worried about leaving, as we technically were overstaying our visa, our train to Kiev crossed the boarder at 4 am the day after our visa finished, but this didn't cause any issues in the end.
-in 2010 at least the embassy in London only accepted payment by postal order!
-We could do the whole process by phone and post.
I really enjoyed Minsk, it was one of my favourite holidays, but that was perhaps in spite of the sights of the city which are mostly limited to Soviet era nostalgia.
We stayed at the glorious Hotel Belarus
it doesn't have the most central location but it had all the Soviet chic we could need.
The In Your Pocket City
guide was brilliant, the Beatles cafe in the suburb was an odd experience.
We organised a tour to Mir and Nezsvizh through Belarus Tour Services
, who I would recommend, they were much cheaper than other tours offered which were preposterously expensive for what was a simple and slightly underwhelming trip.
You can get to the WHSs by public transport fairly easily from what I understand, however the link between the two cities was very tight on time, so we decided on the private tour to fit both into a day trip.