From the specs you linked:
BNC-type rubber ducky antenna
That means you can run any antenna you want. You just need an adapter to go from whatever connector the antenna lead you set up has to a BNC. Radio-smack should be able to fix you right up for a couple bucks.
The specs also say it is 4-watts, which is the maximum permitted power for CB here in the States. That looks like a fine radio. Get yourself a +12VDC adapter and you'll be able to use it in the truck.. then unplug it and put the rubber whip back on and use it away from the truck.
I have a much older, but very similar RS handheld that I use myself. I rarely need a CB radio anymore, so in the rare occasions when I do I just slap a magnet mount antenna on the roof, run the lead through the sliding back window, and plug the handheld into the cig-lighter and use it like that. One handy feature mine has that yours looks to lack is a plug for an external mic. This way I can wedge the radio between the shifter and the center console and use the mic while driving. Works very well.
Regarding antennas, there are a few different kinds. CB antennas are usually classified by size compared to the wavelength of the CB radio carrier frequency. CB works in the ~27 MHz range, which has a wavelength of ~36'. A full wavelength CB antenna would therefore be ~36'. This is obviously impractical, so the most popular is 1/4 wavelength or shorter antennas. But a true quarter-wave antenna would still be 9' tall, still not practical for most of us. So most antennas are physically shorter but use a 'loading coil' to make the antenna 'look' longer, electrically speaking.
Look for a quarter-wave antenna w/ a loading coil at the base. I personally use a 'cell look-alike' magnetic mount antenna. It is probably one of the worst vehicle mount antennas possible, as it is so short (~2'). But it works for my needs most of the time.
I have always wanted a better, permanant mount antenna. But I cannot justify spending money on it for how little I use the CB. If I had my pick, I would go for a Firestik
. They are fiberglass poles w/ the antenna wrapped around it. They are tunable, attractive, and fairly durable. @ ~$25 + mounting hardware and shipping, I find the price reasonable. Given your flea-bay antenna is a lot cheaper..