Cannot determine from description if selected internal PCI sound card would fit inside a Small Form Factor PC

Question

The internal default speaker works but no signal for sound jacks for external amplified speakers. I wish to try two possible solutions.

Solutions

1a. check if this already ordered internal PCI sound card would work and fit with my equipment.

1b. if 1a is wrong is there one that might fit and work? (prefer under $25 at Amazon)

2. is there a USB sound card that might work with my equipment? (prefer under $20 at Amazon)

Note: prices not firm.

Operating System and Equipment

Windows 10

HP Compaq 8200 Elite Small Form Factor

Logitech Z533 120W 2-Speaker Stereo with Subwoofer

ARTIX CL750 Adult & Kids Wired Headphones with Mic (alternate output)

I look forward to your answers.