So, I've been through a few VNs now and wanted some help in looking for more. To try and put what I'm after in simple words: Feels & Romance. I do prefer H-scenes (Not centred around it though, for example I felt like Yume Miru Kusuri had too many.) rather I like them as an element of the story. Here are some of my favourites.
G-Senjou No Maou - Really liked this one, mostly the main route. (In particular I actually didn't get too many feels until the end, but boy was it worth it.) It has also made me want to consider others of a similar 'dramatic' style. Though I still would prefer romance included.
Katawa Shoujo - My first, and so likely biased. But the feels hit me in a fair amount of these routes.
Little Busters! - For some reason, I didn't get the same emotion out of this that people seemed to make me believe I would. Still, I enjoyed it.
Clannad - Again Loved this one, meni feels.
Angel Beats! - LOVED This and the anime is one of my favorites also.
Unfortunately, I'm a sucker for good art and so sometimes I feel like I'm wrongly put off of older VNs. Still, don't hesistate to suggest them.