If you are serious about pursuing a career, part-time or otherwise, in graphics design, you'll need to consider the following.
First of all, the old saw "the client is always right" is not valid. If a client knew all about the niceties of graphics design, he or she would not have needed to hire a professional designer.
Therefore, your client cannot know the best way to create graphics. It is a part of your job as a professional to educate your client when he or she is asking for things that may lead to problems down the road or things that simply don't work. it's up to you, if you care about seeing that your client gets the best result, to inform them of such problems.
Doctors do this. Lawyers do this, and so do many other professions. If your client is unwilling to listen to valid advice, you might be better off advising them to find another designer.
I once worked for a medium-large print shop. We in the pre-press and design department were seldom allowed the luxury to speaking directly to our clients. Instead, we were required to deal with sales reps, few of which had ANY knowledge of what it takes to create a piece of artwork. Often, the sales rep would demand that something be done in a certain way, a way that those of us who actually performed the work knew would be impossible or troublesome, and would produce less than optimal results. Were we to suggest a different approach, the sales rep would sometimes become angry and even more demanding and suggest that if what we built didn't work - which it usually didn't - then it was our fault. And they'd flatly refuse to try and educate the client about a wiser approach. "Just do it the way they want!" was the normal response.
This is an extremely stressful way to earn a living, and it is the primary reason I've retired from graphics design.
All that said, you really need to begin designing your logos in vector format. If you prefer not to use Illustrator - the industry standard - then you ought to look into the several other vector apps now available.
If you begin with a vector design, and you find that you need a non-vector version, it is far easier to convert vector to bitmap. As you have discovered, reversing that conversion, from bitmap to vector, is far more difficult.
I've encountered this problem many times when working up a design for a client and I'd ask them for a clean, print-ready digital file of their logo and they'd shrug and suggest I download the logo from their website. Ever tried to use a web-ready image in a much larger space? As you've discovered, it doesn't work
well.
Begin with vector, always, and you'll find yourself using a lot less anti-acid.....
