In my view its the right decision.
You can always add more later.
On a limited budget, rather than HTIB, I would reccomend buying good equipment that will last, item by item, as budget permits.
This way you get a system that will last many years.
My thoughts on sequence of purchase.
1. AVR receiver + good bookshelf speakers ( theYamaha you have mentioned seems fine).
This itself will give you a massive upgrade over TV speakers.
2. A good sub, when you have the money.
This will upgrade your system from 2.0 to a 2.1 and give you most of the fun of a home thetre system.
3. A matching centre speaker, when you have the money.
4. Surround speakers. These need not be expensive.
You can space this out over months or years.
Just my thoughts.