fusable interfacing is thin- like a layer of muslin (or thinner) which has a fusable web on one side- it adds (body) to a bag without adding bulk- fusable fleece adds bulk
timtex is a stiff interfacing that is fairly easy to sew through (by machine) it comes in fusable and non-fusable forms- it is the same stuff used in baseball cap brims. craft fusable is often fusable on both sides- (used for appliques, ect) which you press to the back of a fabric- cut out- then peel the paper and press to a back ground.
if you want to use an interfacing that is not fusable (but you need fusable) you can always press a fusable to it- like steam a seam lite, heat & bond lite or wonderunder (from pellon) you press the fusable to the interfacing- peel the paper then use as a fusable interfacing.
medium & heavy interfacings are used in shirt collars & cuffs- to give you and idea of their (property/bulk)
since they are your projects you can use what you want- but keep in mind if it calls for stablizer/interfacing and you use fleece it is going to affect the size/bulk of the bag-since fleece is alot thicker/meatier than interfacing which is a very lightweight fabric.