There’s no best way. Your 2 solutions are valid : separate images (that will most likely be merged into a spritesheet for performances sake) and animated ‘puppet’ characters. High numbers of articulated characters can become CPU intensive where ‘precalculated’ animations can eat a LOT of memory quite rapidly.
The optimal way really depends on the style you’re after and your usual workflow for graphical production. You need complexe poses with characters seen from many angles ? You might want to go the spritesheet way. You want simple animations but with really smooth and fluid movements ? Articulated characters might be your best shot. What is your target platform ? How much memory and disk space do you have on this target ? There are some technical and artistic questions you need to answer to choose the correct solution.
The game is a 2d sidescroller, and the characters/sprites will be viewed at from one angle only. My usual workflow for animation and graphics is with 2D so using skeletal rigs and such, never before 2D except in flash. The animations will be simple yes, so a dragon flying or a dragon breathing fire, or an archer firing his bow etc etc.
Target devices are going to be iOS and Android, with android devices there is always a big variety of memory and cpu power.
Well, still depending on the graphic style you’re after, maybe you should use articulated character rigs. Either with skinned mesh animations using a 3D package like what is doing Mikamobile, or using one of the 2D animation plugin available on the Asset Store.
If you know or are an experienced developer, it is also not too much work to create a bridge between Flash and Unity to import animations done in Flash. But it’s certainly not as easy as using an existing solution. You just have to know that Unity doesn’t offer yet a native solution to do that kind of stuff.
The game’s graphic style is going to be cartoony (angry birds/jetpack joyride style)
I have purchased the 2D toolkit, from what I gather from that it uses seperate images which are each a frame of an animation and you pile them in to create one animation. If I am correct is this the best method for me to use?
Hu no. Personnaly for cartoony stuff, i would go the articulated parts way. It seems I didn’t take a close enough look at 2D toolkit. It can do this kind of thing but using the Unity animation system which is… well, not that good for productivity. I was thinking more about something close to http://forum.unity3d.com/threads/124211-Smooth-Moves-2D-Skeletal-Animation. When you use this kind of tool, you also rely on spritesheets, or more accurately just atlases, with the different parts and poses of each part of one or more characters on the same texture.