I had a Nikon 1 V1 mirrorless converted to 720nm IR in 2015, I used it for two years. I used it mainly with the 10mm f2.8 wide angle, and sometimes to 10-30mm kit zoom.
I think mirrorless is a better proposition than a dslr, the wysiwyg viewfinder is very good to work with, as is the correct focus with any lens (no calibration required per lens).
I sold that camera as I was finding the lenses limiting for infrared, edges and corners were considerably degraded compared to the centre.
Earlier this year I purchased a Sony A7 and had it converted to 850nm IR, my interest is in black and white work, there are a few lenses that are known to work well in IR with this system. I've started with a 35/2.8 Sony-Zeiss. It seems good out to the edges, but it has a hot spot issue that sometimes appears at f5.6 and more often appears at f8. Since I shoot landscapes and urban scenes I often want to use f8 for depth of field. Apart from that the camera is already giving good results and I'm happy with it. I need to get a 24-70/4 Sony zoom, it works very well in IR according to most people.
You can see some images I've made with both these cameras in a Flickr album.
Shooting IR with digital (especially a camera with EVF) seems better and easier than when I was shooting Kodak HIE in my 35mm slr back in the 1970s. Processing in Lightroom and Photoshop seems quite straightforward for the black and white work I do. The Nikon 1 camera took more work to get a good looking result from, but the Sony files are quite pleasing and easy to work with.
Of course I've seen good work done with converted dslr cameras, but if you have a choice I'd go for a mirrorless system.