Long-distance electrification would be overhead wire. DC requires frequent substations, which means it's about twice as expensive to build *and* maintain. Third rail also needs to be DC (there seems to be some problem with third rail AC, which is reportedly used in the Moscow subway but has never been used outdoors; I think the problem relates to current leaking to ground?) Furthermore, third rail requires more frequent substations than overhead *DC* due to more current leakage to ground! It also requires more metal (more $$), and so on and so on. (It does also impose a speed limit due to maintaining the 'shoe' contact with the rail, though I can never remember what that limit is; but I'm pretty sure it's at least 110mph, the speed limit of the existing coaches and baggage cars, which means it would be relevant if entirely new trains were used, but not if new locomotives were attached to existing passenger and baggage cars.)
To use it effectively would require acquistion of 'dual-system' all-electric locos which ran on underrunning third rail 750V DC and overhead 25KV AC. (And the overhead electrification of the Empire Connection.) With the exception of the unusual shoe needed for underruning third rail, these exist off the shelf in Europe. Unfortunately the FRA's Not Invented Here rules and the Buy American rules probably mean that until some regulatory reform is achieved these would be very expensive (rather than, as they should be, cheaper than diesels). It would probably then make sense to change engines at Albany for all trains which continue past there, until the electrification can be extended (20 minutes is the shortest scheduled Albany layover, and this is already done for some trains, so this isn't unreasonable, especially if we assume speed increases Albany-NYC, which would be the main point of the electrification).
Again, until NY gets serious and buys the CSX-owned portion of the track from Albany to Poughkeepsie -- which is a minor branch line for CSX -- we're not going to see anything significant happen. That's been recommended as the priority first step by every high-speed rail study or commission, and the state just hasn't gotten around to opening negotiations, which means it's not really serious about it.
My fairly-plausible fantasy scheme had this electrification and track improvement as 'step one', with Metro-North acquisition of more dual-system electrics as 'step two', and re-electrification of the Hudson line on overhead catenary as 'step three'.