The problem is that you have to know what you want it to look like, that's what a designer is figuring out based on your loose ideas. AI tools will also generally not give you a format with any flexibility, you're going to get a bitmap that's not scalable in any way like a logo ideally needs to be (but it could work for the needs here).
For the budget Fivver is probably the best bet, a local designer will likely be 500+ if they're any good.
Ideally you want to have a direction or concept for someone to work from but not be too prescriptive, giving the person working on freedom to explore some different directions to land on something that works.