I also have the D-600 and D-750. They are very similar in a lot of aspects both cameras take great pictures. The most important difference for me is the low light focusing advantage of the D-750 for events. I have used the D-600 for a couple of years now and when shooting events I had to take a lot of redundant shots in poor light because of the high percentage of missed focus. It's not the low light imaging, that's great, it was getting them in focus to begin with. The D-750 is better in that respect and it is a little more customizable and a few minor improvements. In good light both are good cameras. So be confident in the bodies, you've got two very nice ones. I may be assuming too much, but it sounds like you are young in your digital imaging learning curve and you have a lot of fun ahead of you. Go out and use them cameras and enjoy.
There is a ton of free information on the web and of course the cameras manual will have the tech. info. you'll want to understand. I came across a book beginners by Scott Kelby when I just started that was very helpful, I don't remember the name anymore. But that lead me to an annual subscription to his KelbOne on line training where I've learned a lot. The individual classes area a bit pricey but the annual subscription is a great deal if you can justify it. And shoot, a lot playing and experimenting to see what works and what doesn't learning your camera in the process, keep your cameras manual handy at first.
I have been using ACDSee for years for my digital management and RAW processor and am very happy with it. It is very similar to LightRoom but in general easier to use. I might prefer LightRoom's development module slightly better than ACDSee's but they are both very good. I like everything else about ACDSee more, it's just more intuitive for me. I've tried Corel's Snapshot and it's not bad but it's not there yet. I do use Corel's Paintshop Pro Photo when I need a pixel editor and like it as well as PS Elements.
I have owned a D600 for about a year and a half and use it primarily for product and events. The image quality is great, however coming from a D300 if I had to do it over again I'd go with the D800. I personally prefer the D300 body and control layout over the D600, plus it fits my hands better.
The other reason is that in low light the D600 focus performance is not that good. I cannot speak first hand here but from what I've read the D800 does OK in low light. This may not be a concern for what you are doing.
One last thought: I am constantly working around all the focus points bunched up near the center on the D600. It's annoying, a bad decision on Nikon's part in my view.
I have had several lens either back focus or front focus, 1 Tamron and 2 Tokinas. I sent them in under warranty and in all three cases they adjusted and cleaned them and sent them back spot on. I haven't had to send any of my Nikon lens in for this but if they were out I would because I don't want to fiddle with 2 bodies that I can adjust and 1 that I cannot.
I own a D300, D5100 and recently bought a D600. The D600 does have the best image quality especially in low light, but in good light I've printed very nice 18" x 24" and larger prints with the 12 megpx D300. When I got the D600 I spent $4000 for the 24-70 and 70-200 and I'm not willing to carry these lens when flying. They are mondo, great glass but heavy. When I'm flying I'll carry one of my DX bodies with the lighter DX lenses. The D5100 is small and light and has great image quality. It is a little frustrating to use after using the D300 & D600 as far as ergonomics and control goes but I'm totally satisfied with it's image quality. You can achieve a shallower depth of field with an FX format, which when you want it it's great, when you don't you have to work around it. It's a lot of money to step up if you don't have the FX lenses. Don't go in debt to do it.
I own a D300, D5100 and recently bought a D600. The D600 does have the best image quality especially in low light, but in good light I've printed very nice 18" x 24" and larger prints with the 12 megpx D300. When I got the D600 I spent $4000 for the 24-70 and 70-200 and I'm not willing to carry these lens when flying. They are mondo, great glass but heavy. When I'm flying I'll carry one of my DX bodies with the lighter DX lenses. The D5100 is small and light and has great image quality. It is a little frustrating to use after using the D300 & D600 as far as ergonomics and control goes but I'm totally satisfied with it's image quality. You can achieve a shallower depth of field with an FX format, which when you want it it's great, when you don't you have to work around it. It's a lot of money to step up if you don't have the FX lenses. Don't go in debt to do it.