Do you only use commas with conjunctions when there's a second independent clause?

I sort of have trouble with knowing when to place a comma with a conjunction because in a lot of scenarios, it would feel natural to put one there because of the pause.

For example:

I'm going to the store but with no money.

or

I'm going to the store, but with no money.

and

You are good but also bad.

or

You are good, but also bad.

I know a way to make the comma work would be:

I'm going to the store, but I have no money.

But what about in the other scenarios?

Answer

You're not speaking your text; someone else is reading it. Unless the reader is reading out loud, there are no speech pauses. Such pauses as would occur in speech are a poor guide for comma placement. Punctuation should guide your reader into making the correct parse.

A style guide provides general rules for punctuation, and you should thus be guided by yours, either the one you've chosen or the one thrust upon you by editors, professors, and other tyrants. I prefer the Chicago Manual of Style which will advise generally, that you separate sufficiently-long conjoined independent clauses with a comma:

I am going to the store, but I don't have any money.

You may dispense with the comma for short clauses:

I'm in the store but I'm broke.

Likewise, if your conjunction forms a compound element not an independent clause, you generally omit the comma:

I'm going to the store but don't intend to buy anything.

The last sentence has one clause with a compound predicate, am going with do ... intend.

But these rules have exceptions. The first is the juxtaposition of antithetical elements, i.e, two stark contrasts, as illustrated by your example

You are good, but also bad.

Notice the justifiable use of a comma with the compound and contrasing complement good but ... bad.

The second exception avoids a so-called garden path, a sentence that without punctuation may lead your reader to misparse the sentence. Consider

She has the documents and plans to be at your office within the hour.

This sentence has one independent clause with a compound predicate has and plans, but without a comma, your reader is likely to think the sentence has a compound object documents and plans. In this case, the courteous thing to do is supply a comma to guide the reader safely to the right syntax:

She has the documents, and plans to be at your office within the hour.

Another exception falls under the category of similars and identicals, but for conjunctions, my examples have to be somewhat contrived:

I'll accept no ifs, ands or buts, but only valid execuses.
I will now discuss the history of the word and, and expect to take about an hour doing so.

Italics aren't really enough to avoid the somewhat jarring "buts but" or and and.