I kept my 38 footer pretty far up the Severn (Saltworks Creek) for a year and a half and have sailed up the Severn on many occasions. As other have suggested the Severn is pretty deep and is wide enough to sail up easily. Round Bay is large enough that you could spend a quite a bit of time simply sailing around it in a small enough boat, that is if you so chose.
As others have suggested, it is very difficult to make recommendations without knowing your budget, the draft at the dock where you plan to keep the boat, your experience level, or any special interests you may have like cruising over night, or racing, or sailing with a family of four, and of which would be helpful in shaping people's recommendations and so on.
What I would say, as has been implied above, the prevailing winds in the river follow the river. They can be shifty and changable as the winds are buffeted by the shore. There can be mild currents in the river, but nothing scary. Once you learn the river, if you own a boat that points upwind reasonably well, you can get into sync with the river, being able to take advantage of the jogs in the shoals to take longer tacks than you might expect.
As a result, if I were buying a boat to sail on the Severn I would want a boat that sails well in a range of breezes, especially light air, and which can quickly adapt to gusts and lulls. I would want a boat which can point well, and moves well on a run or deep reach. I would want a boat that was relatively easy to tack and jibe. As others have said, there is a height limit to the bridges but that should not be an issue of you are considering boats of a size which could be a 'hybrid'.
Jeff