My wife and I travel to VG, as the locals call it, often because we have friends there. We've found the easiest way to get there is to book a flight to Beef Island, Tortola connecting through Puerto Rico. Once on Beef Island, take a 45 minute ferry to Spanish Town, Virgin Gorda. Just be sure your flight lands well before the last ferry sails at around 5 pm.
Regarding budget accommodations on Virgin Gorda, that's a more difficult problem. VG is a sparsely populated island that has not allowed high rise development, preferring to cater to an upscale market with a handful of expensive resorts. However, if you listener can convince some friends to go with you they could split the cost of a reasonably-priced villa (which is what my wife and I have done in the past) lowering the costs significantly. Villas in Virgin Gorda are listed on VRBO.
I hope these suggestions help, as Virgin Gorda is a beautiful gem and offers a unique Caribbean experience.