A mobile like that is pretty battery-hungry for backpacking. If it's putting out full power from a pack-mounted antenna, you'll need to consider RF safety issues especially on 440.

You can work out all sorts of figures based on the current draw when receiving and transmitting and what percentage of time you'll be transmitting, but in the end, you'll probably find that a 7 amp-hour sealed lead-acid battery makes the most sense. It weighs about 5-6 pounds and you can probably run almost all day on it. It's a very common size for computer UPS's so they're usually the best deal. For a good bit more money, you could go a lot lighter with a NiMH pack that gets 3-4 amp hours. One problem you'll face is that with only 12 volts, most mobile radios are going to have a lower RF output since they are meant to run from 13.8 volts. You can get around that with an 11-cell NiMH pack for 13.2 volts or some companies produce voltage boosters to maintain a level 13.8 volts from a 12-volt battery.

For conserving battery power, a great option is to use a handheld or scanner to receive and leave the mobile radio off until you need to transmit. They draw a lot less power when receiving than most mobiles.

Antenna-wise, there are a lot of options. Any 2m quarter-wave ground plane antenna would work reasonably well on both bands. You could mount one to use the top of a metallic pack frame as the ground plane. A better option is an end-fed half-wave on 2m that won't require ground radials. Something like the Comet SBB-5 is a good choice. It's a half-wave on 2m and stacked 5/8 waves on 440. If you're just planning to operate from stationary points, a roll-up J pole hanging from a tree limb is a nice packable antenna. A portable beam antenna would help a lot, especially if you're just on a handheld radio. Arrow Antennas makes portable beams that pack well, or you can build one even cheaper (Google for cheap yagi).