Posted 10.09.2015 @ 11.02PM (Edited 10.09.2015 @ 11.03PM)
I know this was asked a while ago but just in case it helps anyone in the future.
I previously did work for a not for profit which used SecurePay https://www.securepay.com.au/. I know they got a good deal and SecurePay do run charity programs. Couldnt find any info on their site but i'm sure if you got in touch they could help you out.
Posted 10.09.2015 @ 10.47PM (Edited 10.09.2015 @ 11.26PM)
I give Genesis a thumbs up basically for the points you mentioned. It has great performance, isn't bloated and includes out of the box SEO.
I use Genesis child themes for clients who are happy with a spruced up template. I have tried elegant themes (primarily Divi - http://www.elegantthemes.com/gallery/divi/ ) but it seemed a bit too bloated and out of the box SEO wasn't as good as Genesis.
For clients that are paying for a professional graphic designer i generally code the site up from scratch. I'm pretty efficient at this and I find it much easier to cater for any intricate details the designer may throw my way.