Hong Kong essentially has three main shopping/ eating/ hotel districts. Mong Kok and TST in Kowloon and Causeway Bay on HK Island.
I would definitely choose to stay in one of those areas. Don't be tempted by a cheaper hotel elsewhere. There's a reason it's much cheaper.

Another good choice is Central/ the Mid-Levels, but that is very much more of a bar and club area. A nice place to go for a Western meal though.

You are right that you want to be close to the MTR. HK tourist attractions are spread out, and you will use the MTR.

TBH, If I were visiting Hong Kong for the first time, I would probably choose TST. More to see and more on your doorstep. And that harbour view...!