What about a single edge (SE), like a Gem/Eveready? The 1912/1914 provides close, comfortable, excellent shaves, Injector razors are also an excellent option, I find my Schick injector to be an even faster shave then Disposables what with not having to worry about clogging and not having to bang the razor against the sink to try to unclog it and they shave like a disposible so the learning curve it very slight, you just have to remember NO pressure or they will bite. For a recommendation on DE's knowing how aggressive a razor you are looking for would help, but for a first timer I would recommend a vintage Gillette Tech a nice mild razor that can be found very cheaply. or if you want aggressive The Red tip is my goto Gillette but is quite aggressive and maybe not an ideal DE for learning. Carts IMO give a decent shave, but it is after the shave that is a problem for me with the ingrowns, razor burn and Bumps that develop after the shave. Every mans face is different and will require slightly different techniques, while the disposibles angle it preset and not variable. When you try a Straight you may find that a different angle is needed than what I or others may find ideal, and you can easily adjust to get remarkabley close, comfortable, pain free shaves. With disposibles or carts you use the angle provided by the manufacture which may be the right angle for your face but it sure isn't for mine.

90 days off a cart? Gillette must manufacture their blades with you in mind, you my friend, are a lucky man!