The second set is better than the first because the first is grammatically incorrect. I've worked for (add an employer or company name here) since October. Or you could make it: I've worked since October. All these sentences are correct: I've worked for almost a month. I've been working since October. I've been working for almost a month. I hope this helps :)

“I’ve worked for since October" is wrong.

The second one: I've been working since October. I've been working for almost a month.