While sorting through my closet, I've realized it's time to upgrade my casual uniform of a v-neck tee with a tank underneath. I don't like the way they cling, especially when it's hot out and I'm just not comfortable in them anymore. I just don't know what to replace them with that will be almost as easy to throw on. I know I've read on here in the past (it's been a couple of years since I've been on here so I'm rediscovering everything) to go with woven tops for a more refined look. The first thing that comes to my mind of course is a button down which doesn't really fit my lifestyle. I do realize there must be a ton of other options out there but I don't even know where to start. I have plenty of sweaters and jackets for when it's cooler but it's still quite hot here. The only woven shirts I currently own are a few button downs that I rarely wear and some sleeveless tops that I like but I don't wear sleeveless by itself so I have to throw a cardigan over the top which negates the coolness factor obviously!  

If I could get some specific examples of what I should be looking for (short sleeve or 3/4) that would be easy to wear with jeans and casual skirts that would be a big help.
Thank you!
Eta: I'd rather not have to tuck in