First of all, don’t go to graduate school because you can’t figure out what to do next. That’s a waste of money and time. Classical archaeology is a particularly bad field to enter just because you don’t know what to do next, because archaeology is a really tough field to break into and most likely, you’ll make it back into an office - just with much more debt.
So you hate your current job. That doesn’t mean that you will hate every job ever, or every job that takes place in an office. (Also, most jobs occur in offices, which is why I am always amused when undergrads say they don’t want “office drone” life. Even archaeologists spend significant amount
Don’t look for employment that will look good on a graduate school app - first of all, because that’s a broad question that includes a lot of kinds of employment (depending on what you want to do), and second of all because you don’t seem to know what you want to do anyway. Instead, look for employment that you will enjoy or at least not hate. There’s so much in the social milieu out there that young employees should “follow their passion” or “do what they love,” but it’s all horrible advice. Work is work; very few people love it, and even people who are in fields that they really like don’t get excited to go to work every day. That’s why they call it work.
Read these articles:
[Don’t Follow Your Passion](The Secrets To Career Contentment: Don’t Follow Your Passion)
[“Do what you love” is not great advice]("do what you love" is not great advice — Ask a Manager)
[Why you shouldn’t follow your passion](why you shouldn’t follow your passion — Ask a Manager)
The goal should be to do work that feels relatively meaningful to you and that you enjoy somewhat - not necessarily because it matches up with a passion, but because you like the tasks that you do every day. And some people simply do work that they don’t actively hate, and that’s okay, too. You have a whole life - friends, hobbies, activities, weekends - to build love and passion around.
That said, if you want a PhD program in classical archaeology you usually need research experience, probably including at least one dig. If you don’t have that, then you’re probably not very competitive despite your GPA.
If you are aiming for an MA program in the field, your past indiscretions shouldn’t matter so much since your most recent grades are excellent. An MA program is a good way to get the research experience necessary to enter a PhD program (and also learn the languages you’ll need, since most programs in both the classics and archaeology require reading knowledge of two languages and most programs like to see you as pretty advanced in one and started another by the time you apply).