I will share based on my own personal experience
A HTIB is no slouch in terms of performance, it will beat all TV speakers, computer speakers, home hi-fi speakers (at least the budget ones), etc. I have been using a HTIB with my PC for over 6 years now, and it replaced expensive Logitech computer speakers that were excellent performers in their own right. In other words, you can buy the Yamaha HTIB outright and be happy with it for a long time. Upgrading the speakers will not really improve the performance much, but like I said you can be extremely happy with the performance of the Yamaha.
I also have a dedicated home theater room that took me nearly 2 years to build/complete. I have the Monitor Audio RX series speakers in it, and I started off by buying the floorstanders initially, adding the center channel after a few months, and then adding the subwoofer and the surround channels. Throw in the projector, expensive HTPC with a fully tricked out GPU for madVR, furniture, etc. and you will get a fair idea of how long it will take to assemble something in parts. Also, keep in mind a lot of preparation work will take place like internal wiring, acoustics, etc.
Obviously I'm not making things easy for you, but hopefully I am making things easy for you to decide and giving you clarity in how you want to approach things.
Start with the end in mind, do you want a fully dedicated home theater room, or simply a 5.1 setup to rock with your PC or TV and STB. For the latter, a HTIB will suffice, in fact literally rock. My PC, my 55 inch LED, etc. run on 2 Onkyo HTIBs and performance is excellent beating out the TV speakers, soundbars, computer speakers, etc. However, they will not compare to a dedicated home theater room.
Finally, spend the most on speakers, audio technology is changing so much and new formats are coming in every year, it does not make sense to spend much on an AVR. You will be looking to upgrade your AVR every 2 to 3 years if you want to have the latest audio formats, HDMI specs, HDR, 4K/8K, etc.