Removing ceiling mounted cabinets

Hi -
I am working to convince my husband that we can update our 70's kitchen with cabinet and wall paint. Also I am considering removing a line of cabinets that are mounted to our ceiling and that separate the dining room and kitchen. They connect to a row of wall mounted cabinets and I know we would have to finish that out with sheetrock.

The problem is that the vent hood and gas cooktop are located in the area that I want to change. The counter top is very wide and the gas cook top is fine to remain where it is. I do have concerns about a few things: a) could there be a load bearing issue that needs to be addressed and b) could an encasement be built around the present vent hood or would it have to be replaced with a chimney style?
In order to do any of this, we would have to avoid any major expenses.

Any advice would be greatly appreciated.