I would recommend doing St Barts after your SXM stay rather than before your stay. It works better in that regard.
St Barts tends to be a slower and more relaxing pace with refinement which is a nice finish to a vacation. St Martin can feel a bit jarring after a St Barts stay since it is a completely different feel.
I tend to stay on both islands.
For a 3 to 4 night stay, a hotel will likely be your route since villas will want at least 5 nights. With that being said, some villas such as villa kaloo on St Barts would be considerably less than hotel.
For hotels, it depends on budget. Tom Beach Hotel would be a good choice due to it's location in St Jean and I love their La Plage restaurant.