I never had a tower before, that's what I hope to get.
Please tell us why. Do you just like the looks of a tower?
You understand with a subwoofer or two, you are going to split the signal going to your speakers. Frequencies below X will go only to the subs. Freqs above X will go only to the speakers.
There are MANY great bookshelf speakers out there that work extremely well with a good sub(s). You can put them on a stand or on a cabinet... and they usually cost less than a comparable tower.
Generally, the purpose of towers is to include more/bigger woofers to handle lower frequencies. Many audiophiles have big expensive towers and subwoofers. For music, the subs are turned off and the low bass capability of the towers is used. For TV/Movies, the subs are always turned back on. But the cheapest pair of towers I know of that are capable of playing clean accurate music w/o a sub are $3500.
If you simply like the look of towers, it's OK. So do I. I have towers for my L/R, L/R Surround, and L/R Rear Surround. But it's absolutely not necessary, and I wouldn't do it again if I started over today. And if on a budget, I would not spend extra money for towers to start.
If I were you, I would spend my whole $2k, or very near it, for one big boy sub. Save, save, save... then get 2 big boy Front Left & Right speakers. Save again, then get matching big boy Center. Save again, then get a new AVR. Save again, then get 2nd big boy sub. All your current speakers can be moved to Surround duty.
The idea is to build your top shelf system, a piece at a time, buying nothing you won't be happy with later, (unless you turn into a real audio nut like the people here), and using your current stuff in the less critical positions.