If you go for a technically conservative approach to the Phoenix considering the limited resources of Cochrane's team, then a Titan booster shell with the original internals swapped for some "high energy density" fuel rocket might have been the most cost-effective way to keep the operational envelope of the Phoenix itself close to the minimum required for a "proof of concept" flight.
A powerplant that would be compact and yet "exotic" enough for a quick warp 1 hop in something the size of the Phoenix in 2063 would likely be a gas core fission reactor. Leave the first use of anti-matter fuel to the unmanned "Friendship 1" of four years later for safety reasons (unlucky Delta quadrant races aside).
As for earth return, perhaps a detachable cockpit/re-entry capsule? I like letting what will later be bussard collectors at the front of nacelles function as ionizing plasma-sheath generators to help get the entire vehicle down, followed by chutes or more likely a para-sail, before a final landing thruster burst. A 20th century style landing would be in keeping with a 20th century style launch after all.
Once again, this scenario represents my idea of the most technically conservative explaination of what we see presented in ST:First Contact.