Hey @sravya8 $2k can get you a great purchase for a GPU rig at home to prototype with.
*disclaimer: this is totally my opinion based after trying out a few approaces : )
Note: The thing to keep in mind is this, having a GPU rig is good enough for prototypes, for the long run and big experiments, an EC2 (or bigger machine) is required regardless.
For example, making small tweaks, playing around with small batch sizes work well, but training a big network (convnet specially) can be resource consuming and requires at least a bigger machine equivalent to the EC2 ones
Laptops is a bit less recommended, due to heating / battery and the fast pace of the GPUs coming out. However, there are 1080s now as you have linked to on the GTX 10 series.
Old desktop, I would say a new Motherboard + good Power Supply Unit (PSU) can allow you further upgrade in 2 years from now.
Reserved instances can be a bit pricey ahead of time for individuals : /!
If you ended up choosing GPUs, here is a build I made 2 weeks ago: 1080 rig, this is a decent setup to be upgraded as well. though for the price, I highly recommend getting at least 1080, since
8Gb of memory on a GPU disappears so easily.