Uh, I think you are misjudging the options:
Option 1: Players can create various FTL's that fall under two main categories (Continuous/Discontinuous) and several sub-categories (Flash/Door/Teleportation; Fixed/Non-Fixed). Depending on which spacefaring races 'succeed' and forge stellar empires, the nature of interaction between FTL-capable races, and a myriad of other factors the various initial breeds of FTL will change, fall out of use, or become overwhelmingly dominant as we progress to Epoch III. Each FTL would have its brand of mechanics that best fit its lore.
thomas.berubeg makes a race that uses a Continuous/Non-Fixed FTL that allows them to move via space via simply speeding up to a velocity that is FTL. They can move 4 hexes per turn before their engines burn out and have to wait a turn to recuperate.
Eltain makes a race that modifies thomas.berubeg's brand of Continuous/Non-Fixed FTL that sees them speeding up to a velocity that is FTL coupled with [insert Macgruffin] that allows them to enter an alternate, condensed space/time. They can move 3 hexes per turn continuously.
nutranurse makes a race that uses a Discontinuous/Door FTL that sees them literally rip out wormholes in the universe to make temporary gates to nearby space so long as [insert Macgruffin-gate] is present in the starting system. They can move to any hex within a 2-ring radius of the [Macgruffin-gate]. They can hop-scotch by only 1 gate ("Move from Gate X to Gate Y via first rip-jump, move from Gate Y into Nearby Space Z.")
Option 2: Players can create various FTL's in name only. Lore can be made up to have giant engines powered by lobster tears, or some sort of manipulation of antimatter as fuel, or outright psionic will allowing the spacefaring race to move through space, but in terms of game mechanics/sector wide lore these mean very little. Races will take their FTL foundations from the same source, though are free to explain it however they want (aforementioned lobster-agony ships). At the end of epoch II we will vote to have warp-drive or hyper-drive or gate-reliant FTL be the dominant (read: only) method of long-distance travel.
Warp-Drive would see space-ships somehow enter some sort of alternate state that allows FTL, but keeps them in n-space (normal space). Mechanically this would be represented as "Players can move fleets X hexes." Ships will still be able to interact with their n-space surroundings.
Hyper-Drive would see space-ships somehow entering some sort of condensed realm parallel to n-space to achieve FTL. Mechanically this would be represented as "Players can move fleets X hexes." Ships would not be able to interact with their n-space surroundings.
Gate-Travel would see space-ships entering monolithic gates that take them to other existing gates (or key points, or beacons, or whatever depending on how we hash out the uniform lore). Machanically this would be represented as "Players can move fleets from Hex X to Hex Y or Hex Z, but not to Hex A." Ships would not be able to interact with their n-space surroundings, but travel would be so fast that this hardly matters.
edit: Added examples of how option 1 would be modeled mechanically.