The caveat to the below is that Bill is correct: There are too many variables to reliably answer a question this broad. But IN GENERAL:
A combo jack shouldn't affect your microphone signal quality in any meaningful way. Jack size starts to matter when you need physical robustness, or are dealing with large amounts of current. The combo jack on a PC or laptop does not need to meet either of those requirements. Current in a mic signal is ridiculously small, so the difference in contact area between a combo and discrete jack is negligible. The only way for it to matter would be if there was somehow crosstalk between the mic and speaker signals, but laptop construction is so compact to make that a risk even with separate jacks. So short answer: No, a listener on the other side of your microphone will not notice a difference between a combo or discrete mic jack.
Your second question starts to get at the heart of the matter: Microphone quality. This is arguably the single most important factor to a clean feed for your listener. A good mic positioned proper distance and direction from your mouth will be worlds better than any built-in microphone. But remember that "good" does not equal "expensive"! On video calls at work, one of the clearest voices was simply using the mic on his Apple (could have been Samsung) wired earbuds, while others with expensive office-focused headsets or even supposedly-decent desktop mics sounded noticeably worse. This comes down to space and design. Mics on mobile headsets are designed to be (and usually are) a certain position from the mouth, and to expect and deal with open spaces and background noise. Office headsets are, too, but for some reason many of them do it poorly. Most microphones are extremely sensitive to echo, and all have their own pickup patterns and frequency response curves. Some have a certain amount of noise-canceling built in.
If your goal is to be heard clearly by others through your PC, the easiest, most reliable way I know of without spending a bunch of money is to get yourself a reasonably recent pair of Apple/Samsung wired buds, preferably from the Galaxy S series on the Sammie side. Second is to grab a USB microphone. Blue is pretty good, and Samson is okay, there are certainly others I'm not familiar with. Interestingly, I have an
ancient Logitech desktop mic (see below) that genuinely impressed an audio nerd (as in, went to school for audio production) friend with its output quality. But no matter what you choose, record yourself talking and tweak your settings, setup and space to get a sound you're happy with. But keep in mind your voice will sound weird to you when played back.