The battery in your avergae cig-alike will last about 6 hours or so - 1 cartridge will last about a day for an average vaper, so what you've experienced so far is prefectly normal.
It's possible to refill cartirdges with e-liquid - use a little screwdriver to lever off the white plastic end cap and drip e-liquid into the cartridge and you're good for another day.
Prefilled cartridges are *hideously* expensive compared to filling your own cartomisers with e-liquid or using a clearomiser.
Lots of people find that they like the vape from a cartomiser and Boge cartos are around the best around, though SmokTech are also pretty decent, provided you don't run it dry and burn the insides a carto can last a week or 3 before needing replacing, though topping it up often can be a pain. Hence CartoTanks were born. Which are larger diameter plastict tanks that a cartomiser fits into. you punch a coulple of holes in said cartomiser fill it and put it into a tank then fill tank with e-liquid an the liquid in the tank seeps into the carto and keeps it nicely topped up for a day or more.
The most popular things to use over here are clearomisers - the main 3 types are CE4 type (avoid these if you can) EVODs and Vivi novas. An Evod is a bottom coil design and gives a cooler temperature vape. A vivi nova is a top coil design and gives a warmer vape. Evods are designed to fit neatly onto eGo style batteries. If you are looking at vivi novas make sure to get Vision branded ones as they are generally much better than all of the knock off vivi novas.
Next up from those are ProTanks. There are version 1 ProTanks and also version 2 ProTanks. V2's are more 'takeapartable' but they are essentially the same design, similar to an evod but more robust.
for batteries there are eGo style batteries. Make sure to get either a Joyetech/SmokTech/Vision branded one rather than a cheap knock off as they are made better and last longer as well as using safer higher grade internal batteries. I can't recomend a VV (variable voltage) version highly enough they are a lot better than the standard fixed voltage counterparts and more than worth the extra. they come in 650mah 900mah 1100mah 1300mah sizes and the bigger the number the larger the nattery and the longer it lasts between charges. Whether you end up getting a larger mod eventually or not eGo batteries makes pretty great backup batteries as well as being small and portable for the times when you don't want a larger device.
Next step up from there is an SVD a Vamo a SID or a ZMax - all of which are virtually identical function wise, they vary a little in the looks/cost department but they are more or less the same size and do pretty much the same thing. Which of those you like the most depends on personal preference mostly. There are also 'box mods' like the itaste MVP which take the same batteries as the tube mods do but are a 'box' shape - usually around the same size as a fag packet.
If you really want to get the best quality device then you're probably looking at a ProVari which will run you a lot more than the devices listed already. Though it might be wise to wait on some of the DNA20 devices that are just coming onto the market from the US to be more widely available here.
Finally the other path to choose is a mechanical mod. All te devices I've mentioned so far are regulated. They use electronics to regulate the power that gets to the coil. Mechanical or mech mods don't. Personally I'd recommend a regulated mod to get going with then when you find the settings you prefer to vape with look at mechs afterwards. Everyone has different taste and it's much easier to experiment with higher and lower power settings on a regulated mod than it is to do the same on a mechanical one.
Welcome to the planet and congrats on switching away from the tobacco.
Sorry, I just noticed your initial reply. Thanks so much. It as per my original reply seems to be making far more sense. I think I need to digest this all a little and decide which route to go but this is making it a far less daunting task!