Barrier coats typically help prevent blisters from occurring or reappearing once you've experienced them. It's done over bare 'glass, not over any paint. Some primers are called tie coats, because they're designed to work over the various types of bottom paint. These are used if you can't identify what you have, but mostly they're a marketing tool to sell you one more product, that a pro wouldn't need. A tie coat is basically a primer and not entirely necessary if you old anti foul paint is in reasonable condition and not too thick. As a rule you don't want to remove all of the old bottom paint unless it's too thick or poorly adhered.
A solvent may not remove all the old paint, especially if there are many layers. Sand blasting can damage the gel coat, so I'd recommend a softer media if going this route, maybe coke, soda ash or walnut shells, instead. You can use a chemical stripper, which works though it's important to use a stripper comparably with 'glass surfaces.
The approach you use, depends a lot on the size of your boat too. Hand sanding after a solvent wash, on a 35' yacht is a career choice and decidedly not time effective, but just an afternoon on a 18' bow rider.
Again, the type of paint you use is area/application specific.
At this point it would be helpful to know what boat you're working on, how many layers of previous bottom paint there are, how well stuck these layers are, etc.
It's common for ablative paints to oxidize once out of the water for a while, which may cause it to chip and flake. If the underlying paint is still well stuck, just sand off the last two coats of paint and apply more. The only reason to remove all of the paint is if you have too much bulk, damage, blisters or other reasons the paint can't be trusted any more.