First, any designer worth their salt should be able to get you what you want. Sending art that doesn't look professional to be printed on a shirt doesn't transform it to good art if it's screen printed, dtg printed, embroidered, etc. So, if you don't feel like you have the skill to do it ... letting someone else design it shouldn't be a issue since you would be paying for their time (if they charge you for it) just keep in mind though, that without an intellectual property release it's their artwork. NOW if price is the issue, because you might get charged ... keep in mind how long it will take you to do the artwork, and how many revisions it will take for your work to pass quality control from a shop (or their specifications) ... your time is money as well and if a shop charges you to create artwork ... it's a one time fee. Also, you can pay others to do the artwork as well ... there are plenty of freelancers out there that do wonders and don't cost a foot and a leg to get custom work done.
As for saving you as much as possible, that is a catch 22. Your best bet for saving money to earn the best profits is not to skimp on quality but to increase quantity of each run. The best part of screen printing for the client is bulk discounts ... once the screens are set up, and initial man hours covered ... it takes the same amount of time to print a shirt each time so the distribution of initial cost of setup is larger (whether that is seperate screen fees or built into the shirt cost ...) making the total cost go down (along with other factors) BUT the bigger the run, the more you initially pay since 40 shirts at 10 bucks vs 100 at 7 vs 1000 at 5 (just an example) will cause most people to go for smaller runs initially especially if you can't sell 100 or 1000 shirts to get the max profit ... especially from one design. Even retail stores try to max this out by getting the same 20 designs in each of their stores ... but only a handfull of each design over a run of THOUSANDS of shirts in each design to get it low enough in initial cost to sell only half at full price before they discount and discontinue the line.