I've never dealt with this, but I can tell you what I would do:
If you already have a printer lined up, ask them for the print specifications. If you don't already have a printer lined up, find one and ask them for the print specifications. I'm sure most are accustomed to clients sending them artwork and they will lay it out for them on their template. However, I'm sure if you ask nicely enough they will provide you with a template.
The template is going to vary based on the size and shape of the mug. Is it just a straight cylinder? Then the template is likely just going to be a rectangle. However, if the mug is tapered then the design process gets a little bit trickier.
Before you create your design, it is important to know a few of things:
What is the print area?
I would ask for the size of the print area as well as the outer circumference of the mug they supply. It would also be helpful to know what the margins are. This way you can create a render as close as possible to the finished product.
What colors are available?
Spot colors? If so, how many can you use per design? Is a color library (such as Pantone) used? Is four-color (CMYK) process available? Since you asked about color mode: when in doubt, use CMYK (for printing applications).
What is the printing process?
I don't know the different printing processes used for mugs, but you should know which will be used prior to designing. For example: If it's four-color process, you don't have to worry about much. If it's pad or screen-printed, then if you want gradients you need to use halftones.
Design in vector format
Vector format is always preferred. That way, you don't need to worry about what DPI to design in. I can't imagine you have an incredibly complex design in mind for a mug, so if you're not comfortable working with vectors then maybe this is a good project to learn. Your printer will thank you for providing vector format artwork (some even charge to convert it from raster if necessary).
Cylindrical printing is not the same as flat surface
When you wrap artwork around a cylindrical surface, it's not going to look the same as when you look at it on a flat monitor. You may find that scrunching the artwork horizontally makes it look better once it's curved. You're on the right track with plans in mind to create a 3D render, but I would go a step further: print it out on paper and make a "paper mug" so you can see what it looks like cylindrically.