Your answers are in your Owner's Manual. If you don't have one you can download one in .pdf format from the Chrysler web site. Comes in handy, especially for searching. I have bookmarked one for my van, use it regularly for myself or answering Posts on here.
Edit: A link to your Owner's Manual:
A search of the Manual brings up 5W-30 motor oil three times, 5W-20 zero times.
Using synthetic oil every 3000 miles is "belt and braces", but more than that, wasteful.
5W-30 is a more robust oil and was likely the one specified back in 2012. They specify 5W-20 for my 2016 now (long story) but Chrysler says 5W-30 can be used, so the no-brainer, for me, is to use 5W-30.
Brand name (my preference for what's in the additive package, another long story) synthetic or conventional oil, meeting API specs is fine. I consider synthetic a waste unless going for 2X conventional oil change interval, so I use it sometimes when I want to waste money.

Some conventional oil, like the Valvoline Daily Protection 5W-30 I use, contains a bit of synthetic (blend). It's often on sale at Walmart here.
Oil monitoring systems, if yours has one, will show somewhere between 5000 and 10000 miles for an oil change interval depending on lots of idling time or lots of highway time. I do about 50% highway driving timewise and use 10000 km (6000 miles) as an oil change target. That's a bit wasteful but an easy number to remember and gives me some leeway (sometimes 1000 km leeway but don't tell anybody).
So, for you, 6000 miles, using Valvoline Daily Protection, 5W-30 should work just fine, maybe a little wasteful.

First off though, I recommend checking your oil level frequently to determine if any needs to be added between changes. In which case, oil change intervals could be stretched out a bit, depending.