Will a GDDR3 bottleneck a Core i5-2400?

I've been researching on parts for a new build. This is the list so far:

ASUS P8H67-M LE Motherboard
(4GBx2 modules) 8GB of 1333Mhz DDR3 RAM
Intel Core i5-2400 Processor (not planning to over clocked, stock clocked at 3.2Ghz)

As for a graphics card, where a live, there is a huge difference between DDR3 and DDR5 graphics cards, and the cheapest GDDR5 card exceeds my budget.

I will use this PC mainly for video editing, image editing and for music software like FL studio, and maybe some light gaming.

Will a GDDR3 graphics card (right now, im looking at an Nvidia GT440) slow any part of my system down?

It's not the GDDR3 that will make the card slow, it's the narrow memory bus and crappy GPU. It seems like you fell for some marketing gimmicks. GDDR5 is about twice as fast as GDDR3 but memory bandwidth is not even close to important as the GPU itself. GT 440 isn't very good at all and it isn't just because of it's memory. Typically cards with better memory have better GPU's.

The GT440 will be fine if your light gaming is Counter Strike, COD, games that aren't demanding at all. It won't slow down your system, unless if you are gaming.

So for processor heavy tasks, i wouldnt be limiting the i5-2400 and wasting it's power by giving it a crappy GPU, correct?

Do you think going with an i3-2100 is more effiecient in this case?

The GPU cant limit a CPU really.