you are not wrong about the merging thing ... my 3d printer uses G&M code which is transferred in by a serial port (easy for any microcontroller) in fact the actual string sent is "G28/r/n" (/r/n is the enter key!)
from a hobby standpoint arduino is simpler ... it is prebuilt and pre coded when using arduino i dont set up the clock speed, or any of the config bits ...ect ... usually there is an H file driver and just a few lines of code to each peripheral i add ... and mostly only a few jumpers to hook everything up .. debugging is limited to serial output data, or a led i have hooked up (and coded)
with pic it may start on a bread board but would need design/transition to my own pcb, it needs a programmer, voltage control & support circuitry, and config set up .. it is way more advanced for debugging and breakpoints are very handy ... also it has been a while since i used a pic but i dont think it comes with h files which means understanding and building the protocol from scratch
i'd say with anything prebuilt is faster cheaper more stable than my own but limited to its own design specs ... and doesnt always hold up to my imagination.
...if you are wanting to spend time and learn more then use pic,
if you want to get er done then use arduino,
when you ask about BT and wifi it is really up to your criteria, in general i suggest wifi too, but you can get cheap chips for both... btw just cause a wifi chip is for arduino doesnt mean you cant use it on pic ... you just cant use the same H file.. instead you need to figure out the protocol it uses and code the pic accordingly.
when you are talking about using a cellphone/tablet to display data you will either need a generic receiver app which will just spit out the numbers
... or you will need own programming so you can send data with a button on the screen, or make an icon appear when data is received... ect ... which is different programming language
For you i would suggest going with the Arduino, it cuts a layer of work out for you and will be alot easier to get started ... starting with the first step of running a blinky code ... just to get your first LED to flash.
examples of pic and arduino projects:
1) PIC .. only 1 sensor on 2 wires ... external voltage controller and data port connection on the catV
2)arduino stacked up with lots of sensors & shields .. and i have only used 50% of the pins available!
3)PIC .. lots of channels needed to run each led individually (5x5x5x3 # of switches being controlled)