Quite easily; you look at them. If there were a way to programmatically define a good logo, there wouldn't be so many bad logos. I don't mean for this to sound facile, but it is like looking at art, or writing: it is very difficult to create a meaningful definition of what good is, but it is often very easy to classify things as bad and not-bad (if not good and not-good).

It probably isn't worth spending $$$$ on logos. But you should care about design as an extension of caring about UX. If your design taste is sufficient that you can produce a simple, acceptable logo - great! If it isn't, it is possibly a warning sign that you need to involve someone who does have that design taste - and not just on your logo.

To head it off at the pass - yes, some start-ups have succeeded with weak design (although far fewer than you think - simple is not necessarily weak), but start-ups have succeeded under all sorts of circumstances. It doesn't invalidate the principle that a good user experience is very valuable to any product.

It's not about money. Big budget logos can suck too.

Often simplicity is the beauty of it. For example, simple code that works effortlessly isn't necessarily creative but it could be and when it works, it's beautiful. Because it's simple should it be cheap? Expensive? I don't think there's a correlation there.

Beauty can be the intricacy of simplicity.