There's no problem whatsoever in mixing bodies, such as a FF with a 1.5x; they both take the same lenses,and today's Nikon batteries offer incredible life. Battery life is no longer a worry, like it was back in the D1 days. I see the OP has no speedlight listed...many times you will need supplementary lighting to get the kind of DOF/image quality that most editors want for color.
If I had to use a D60, I would want a faster lens than the 18-55, like the Tamron of roughly the same length,but with an f/2.8 maximum aperture. The 55mm f/5.6 maximum aperture limitation of the 18-55 kit lenses is just way,way too slow for indoor photography unless you're using flash.
A good, fast prime lens like the 35mm f/1.8 DX lens would be useful, and the 85mm f/1.8 AF-D is a good Nikkor lens to have for many indoor events. Myself, I would be greatly tempted to ditch the D60 in favor of a body that is a bit faster in operation and which has more compatibility with the entirety of the Nikon lens lineup.
Being limited by the f/5.6 maximum aperture of consumer-level lenses means you'll need flash under many situations where with faster glass you could shoot ambient light.
In my book f/2.8 is not exactly "fast",since f/1.4 and f/1.8 and f/2 primes exist at 28,35,50,85,105,135,and 200mm. Since you're a beginner, I'd say buy the two most-affordable fast primes, the 35mm 1.8 and the 85mm 1.8,and see what having a FAST lens can do for you. However, compared with the f/5.6 limitation you're under now, even f/2.8 zooms are relatively "fast" lenses.
As soon as you can afford it, try and move to a D700 or other killer high-ISO body. The elevated ISO's of the D700 and D3 are incredible,and in my day we would have absolutely killed to have had the ISO 1600 and 3200 capabilities of a D700. Maybe by the time you're ready for it, used D700's will be really affordably priced.
My advice would be to ask other,more-experienced shooters for a bit of guidance. You'll probably see that many of them are using older, less-high-end Nikon bodies, often with the old 28-70 AF-S on there, while more established and better-payed guys have the new 14-24 and 24-70. Knowing where to stand is more important than what you're shooting,and making sure you work around/not in conflict with the TV crews and other shooters at crowded events is important; being a PJ is not being a low-rent Los Angeles pap. You need to learn how to act professionally and dispassionately and to get the shots you need, while being sensitive to your subjects and their situations.