I am graduating with an engineering degree in a few weeks and as a graduation gift to my self I am going to upgrade my HTIB.
Welcome here!
First things first, don't graduate with debt or frivolous expenses. The system can wait till you have a few good paychecks tucked into the account. In the meanwhile, audition at stores, ask forum members to give you demos and basically, understand what you like what you don't like (acoustically). Moving up from an HTIB means, pretty much anything decent will be a step up. So, educate yourself on what constitutes good sound, value for money, find deals, etc.
I have been looking at klipsch online mainly because they look "pretty" however ... My biggest priority is accuracy with the sound.
Sending mixed messages here

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Is your budget $4000 or $6000? Pick a number and stick with it. Believe me, I can happily ring up a $10000 system and make you feel like anything less is a POS. And conversely, a properly set up $2000 system can be more than sufficient and make you question the need for a bigger budget. A good rule of thumb on budget is 70% on speakers, sub, 30% on receiver/ pre-pro+amp and as little as possible on cables (avoid the $150 HDMI cables, $5/ft speaker cables, etc.). In speakers, spend the max on main L, R and subs. If the room is large, you will need two subs to get even bass.
First select the speakers and then the receiver, not the other way around. This is because the capabilities of the speaker drive the necessities of the receiver or amp.