I'm not the one to describe a bookshelf system so I'll deal with other parts and you can add your bookshelf speakers with what's left over.
Marantz SR5007 $750.00 (AVR)
Emotiva XPA-5 $900.00 (Outboard Amp, to be added "IF NEEDED," after system is set-up, running and dialed in)
HSU 12" sub (2) VTF-3 MK4 ($800.00 ea) $1,600.00
Wire and interconnects paid for with general, day-to-day budget money; it's not a lot; <$200.00.
(Prices above are based on U.S. availability and priced in USD.)
$2,350.00 - $3,250.00; $2,350.00 if you don't buy the outboard Amp at onset.
Add to the mix your bookshelf speakers as you wish or buy the front three first (you'll still get gripping/engaging sound) and add the surrounds later. IIRC, approximately five percent of all 5.1 content goes through the surrounds. A system doesn't have to be built in a day.
My opinion, the center channel is the most important part of the 5.1 speaker chain as eighty-five to ninety percent of dialogue content goes through the center channel. The next most important part of the speaker chain are the subwoofers and yes, for even, tight sound, one "NEED's" two subs. I repeat, not one but two. My preference is a pair of 10" subs (tighter and more responsive to the bass line) but 12" subs are noted for digging deeper; compromise. I'm a fan of sealed subs in smaller rooms
for tighter bass with a flatter response over ported subs for larger rooms and larger sound. From this list, with monies leftover, buy the bookshelf speakers which meet your fancy. Again, you can buy the front three (L/C/R) and later add the two back surrounds. To the best of one's ability, they should buy the best quality they can afford and if that means not buying a pair of surrounds at the onset, then so be it. Your sound will be rewarded for your patience.
No matter what you choose to do, don't be in a hurry. Read as many reviews as you can stomach. Audition as many speakers as you can. Respect the stores you audition with; don't use them as an audition store and then buy online. That's unethical. You have plenty in your budget to buy wisely and good luck.
Hope the above helps in your decision making process.