Welcome to the forum, Jdown!!
Don't worry, as Vattené said, this is very manageable.
My first piece of advice is to get a firm handle on your spending and budget. I recommend doing two separate things to do this.
First, calculate your monthly take-home income. Then calculate all of your fixed monthly expenses: mortgage/rent, utilities, insurance, any monthly memberships you have, minimums on your credit cards, just anything that you absolutely have to spend every single month without fail unless you make lifestyle changes (for example obviously a hypothetical gym membership or Netflix subscription aren't vital life expenses, but include them for now if you're already signed up). Next, calculate a realistic estimate of variable expenses like groceries, entertainment, gas, etc. Now total up all your expenses, fixed and variable and compare that to your income. Does it look okay, or does it fill you with a cold terror? (J/K....I hope). Whatever you have left is your preliminary estimate of how much extra you can throw at your credit cards. I very much agree with Vermonster that you should focus on paying down your highest interest card first. That definitely makes the most financial sense and will save you the most money in interest. However, don't dismiss psychological factors if you're pretty sure for example that starting with your lowest balance card and paying it off first will help keep you motivated - or alternatively if staring with your highest balance card and making a dent in it first will keep you motivated. Pay toward the highest APR first if you feel like you don't need extra motivation, but do what's going to keep you trucking along.
Second, as a completely separate exercise go through all of your credit card and bank statements (I recommend going back at least 3 months or more) with a fine tooth comb. Categorize all of your spending, especially compared to the list you created above. Did you maybe forget about a fixed expense? Did you estimate $300 a month for groceries only to realize you've actually been spending about $600 a month? This information can help you see areas for improvement and potentially allow you to shrink or expand your budget as needed. So for example if you have been spending $600 a month in groceries and only budgeted $300, maybe you can actually slash your grocery bill in half, but maybe you need to adjust your budget to $400 a month. Personally I'd rather give myself some wiggle room and have a realistic figure than miss it and feel terrible (and demotivated). If anything you might consider setting a FINAL goal of $300 a month, but giving yourself 2 or 3 months to gradually get there. Like $450 the first month, $375 the second month, then aim for $300 in the third month after you've had a chance to adjust and look for ways to save. Now is also the time to eliminate any fixed but discretionary expenses, especially if you don't have nearly as much money left over as you'd like to apply to your credit cards. Do you really need those hypothetical gym and Netflix memberships (or whatever fixed expenses apply to you)? Can you get by without cable TV? Is your car insurance bill too high and maybe you could get by with more basic coverage? Is your house or apartment a money pit and maybe you'd be better off long-term downsizing?
In the short term don't worry too much about your credit score. Make sure you always pay at least the minimum, on time, every month on all your cards and bills, but don't worry about utilization right now. You don't need to worry about getting approved for additional credit cards, a car loan, or mortgage, etc., because right now you need to focus on paying down your debt and the last thing you need is more debt/a new debt instrument.
The only exception to this advice is if you think you might need to open a 0% balance transfer card, like the Chase Slate for example, or perhaps do a low-interest, peer-lending loan like through Lending Club (or a conventional debt consolidation loan through a bank or credit union). In that case, of course you need the best score possible to get the best terms possible, and indeed that could potentially save you a lot of money, but regardless you definitely need to start by creating a budget, and analyzing your recent spending.
A very simple thing you can do in the meantime: resolve to never go in the wrong direction again on your accounts. The last thing you want to do is pay $150 to one credit card only to charge $90 on each of the other two. Resolve that your balances, on ALL cards, is only going to gradually get smaller.
Anyway, best of luck and keep us posted if you can!