I'd go for:
(Pricing is from amazon.co.uk)
First rate lenses that will still be first rate in 10 years or when you get an FX body, and a basic camera that will do everything you need for almost anything a serious amateur would care to do (plus lots of nice features not even conceived of when your D60 came out.)
Edit: yes, I mean skip the FX for now. Better lenses will do a lot more for your photography, and the D3200 will be a big step up from the D60 in image quality. Note that you'll get very solid ISO 6400 performance from the D3200, which will address the low light issue nicely, your 35mm lens will still be an excellent fast normal lens, and the extra stop or so on the pro zooms will be a huge help for both AF performance in low light and pushing farther into darker environments. Finally for a LONG lens you can use your current zoom, though it's very rare I'd go past 70mm on DX for the photography you're doing, including portraiture. If you need a long lens, the 70-200/2.8 is an option later on.
Here are the reasons to go for a full-frame sensor:
Shallower depth of field effects (though this is very subtle coming from a DX sensor)
Access to very wide angle lenses (though current lenses are much wider than they were a few years ago due to DX popularity)
Better extreme low light performance (though going D60 -> D3200 and going for 2.8 zooms will get you most of this advantage too.)
Pro features like older lens compatibility. (which are mostly just nice to have and not going to be make or break for you.)
I personally went for a full-frame camera only after having pretty much all the lenses I wanted, and mainly because my lens choices were mostly made when I was shooting film. Plus, I love wide angle photography and my widest lens was a 17-35/2.8 zoom. I could have gone for the 14-24/2.8 to address that, but given the whole picture it made sense to go for a D800 instead, particularly since almost all my lenses were from before AF-S became common.
TL;DR version: FX sensors are great, but top end lenses and an inexpensive modern DX body will get you farther for less money.