I'll answer you in general since every vape site is different and while most of us use a standard vernacular many terms can often be misleading or used in different ways.
In generally a "rebuildable" is something that you, yourself, will build and rebuild. The generally means that you are responsible for building the coil, testing it, wicking it, then applying juice. Rebuildable can refer to drip atomizers with no wick, with a wick, and with or without a tank. You also see many people rebuilding standard coils. Myself for instance used to rebuild my Aspire Nautilus coils b/c I hated the stock coils. There are tons and tons of videos on YouTube on how to do this.
RBA, RDA, RTA, and the like are for advanced vapors only. I hate using this terms but it seems to be the best one I've come across. Simply put you only want to move into rebuildable atomizers if you have fully educated yourself on what you are doing, the basics behind Ohm's Law, and have a decent experience vaping an standard devices. Since you will be building your own coil, adding your own wick, and then vaping it you want to be fully certain you are doing it correctly so you don't harm yourself in anyway.
I personally only drip. That is I use a mod (my personal fav is the IPV2 right now) that can supply a good deal of amps (on my device configured by changing the watts supplied) with a rebuildable dripping atomizer (RDA, in my case currently a Stillare). I build my own coil, test the resistance, wick it, and then drip liquid onto the wick until saturated, apply power and vape the goodness that results. RBA's and RDA are tankless while RTA have a tank. All three need to be built and used properly.
If that is something you'd like to get into, great. I love it and have not gone back to standard devices since. However, do yourself a favor and ask a ton of questions. Read everything you can on the subject, and watch a few YouTube videos before you start. If you have a reliable B&M near you stop in and see if they can help you get started with rebuilables. But be prudent in your own education. I've come across a number of vapors looking to get into building, dripping, sub ohm, mech mods, etc., whose local B&M just sold them whatever they could, patted them on the back and sent them out the door without really instructing them on safety and how to use their new equipment.
Now in terms of you not carrying coils or saving effort. Rebuildng may not be for you. Sure you can build a coil or set of coils quickly once you get good at it, toss a wick in and be on your vaping way in less than 10 mins, but depending on how you vape, how often you switch flavors, you may still find yourself maintaining a RDA just as much if not more.
As for your coils going bad. I've always been a fairly heavy vapor. I used to keep a pack of coils at my desk at work and a box of them at home. That way I always had one should I need it. Depending on your vaping habits you may be just going through coils that fast and honestly there is really no way around it. Amount you vape, type of liquid you use and how high (volts/watts) you run your coils all contribute to coil lifespan.
I love dripping and building. But to be honest I carry more equipment with me now then when I used standard equipment. I never leave home with out at least my basic build kit with me just in case.
Feel free to let me know if you have any other questions or if you want more info on how to get into building. I love to vape and talk about vaping, so feel free to ask away.
Vape on!