I have both - an old Mini-14 and a 6.8 mm AR-15 that I built about a year ago. I've shot tons of stuff out of the Mini w/o a single issue. Even cleaned it a few times over the years.

Mine isn't all that accurate, but there's an attachment that you can buy that cuts down the barrel whip and improves accuracy quite a bit. I plan on springing for one, but don't have the website handy at the moment.
I'm not a fan of AR's in general. They are touchy about what they'll shoot and can be a bear to clean, especially in/around the bolt and bolt carrier. But it was fun to build. You can get uppers in all sorts of calibers. I decided to build mine because I wanted a 6.8 mm carbine and got a great deal on an LMT upper, but also am saving towards a .50 Beowolf upper for it. Don't plan on getting a 5.56 upper. That's what my Mini is for.
As for bargain basement AR-15's, that's exactly all you get. As I said AR's are touchy beasts. A cheap one probably won't shoot as nice as a Mini and certainly won't be as reliable. My experience is that if you pay cheap, you get cheap - especially with firearms. Better to save up a little longer and get something that's reliable and will last.
I see .223 as a fun plinking round and nothing more. You can get .223 dirt cheap in mass quantities. That suits the Mini-14 very well. The 6.8 AR is for serious shooting. If it was a 5.56, it would just be another plinker.
My recommendation: but a Mini 14 now with Ruger magazines (they run sales on them occasionally) and build a nice AR-15 later in the caliber of your choice.
"To disarm the people is the best and most effectual way to enslave them" -George Mason, American Statesman (1725-92)