Arduino is going to be the easiest, though not necessarily the best. The Atmel MCUs the platform is typically built around are good parts. Arduino is mainly a software platform that supports a C programming environment and an easy to use interface. Though, there is an amount of hardware dependence involved.
Arduino carries a lot of interface hardware along with it that can be size prohibitive for an e-cig mod. To resolve that, you can ditch the supporting hardware and design your own PCBs using an Atmel MCU with the Arduino bootloader pre-installed. In that case it's probably going to be as compact as anything else, though the MCU program memory requirements are higher to support all the stuff that Arduino carries along with it.
The Arduino IDE (integrated development environment) is all open source so you can download and use it for free. You don't need a programmer/debugger for the Arduino boards, but if you want to ditch the supporting hardware, you will need one to install the bootloader on to a blank chip. I believe you can get bare MCUs with the bootloader already installed which saves you the need for a programmer/debugger. The basic Atmel programmer/debugger is around $50 I think.
Another option for an inexpensive MCU platform is from Microchip. In that case you have the option of programming in C or assembly. C is pretty much industry standard, but assembly has its advantages and some disadvantages as well.
A programmer/debugger is required for the Microchip MCUs and they're also about $50. Microchip offers a free IDE called MPLab that's pretty good, at least I think so.
The main difference from Arduino is the interface and programming environment is not as seamless. Also, the Microchip parts use either a JTAG or ICSP interface to program the MCU where the Arduino uses standard USB. The advantage with the Microchip stuff is you only load what you need for your program to run so there's less overhead and lower program memory requirements.
There's tons and tons of different MCU architectures out there. Those two are the more popular ones for hobbyists since they have the lowest costs involved.