First keg, carbonating question?

You have time to go "low and slow" if you want. Personally, I can't tell a difference between the two methods when it comes to ultimate outcome.

 

It usually takes me 10-14 days to get the desired carb when I set it low and slow, usually 10 psi. You might want to set it at 30 psi for 2 or 3 days.

 

When I set PSI to serving pressure it takes 2 weeks to fully carb. I would bump up the PSI for a couple days to speed things along.

 

I usually hit it with somewhere around 20-25 psi to seal the lid and then drop the psi to serving pressure. It is usually ready to go right around 15 days.

If this is your first keg, make sure you don't have any leaks, check the lid and the disconnects and the pressure release valve.

 

My tried and true way has been keg it after a cold crash (~40F or so), set it at 30psi for 24hrs and then reduce to serving/carb pressure for another 24hrs. Usually it's pretty close after that. Usually spot on after a few days, but the 30psi gives it a jump start.

 

For the carbing, as everyone has pointed out you can go high for a day or two then set it at dispense pressure and wait.

I want to add that you will probably enjoy the beer most after a few weeks of keg conditioning. Yes, lager your keg. There is a sweet spot with all beers, ales included, after a few weeks of conditioning. Green beer needs time.

So be aware with kegs there is usually a noticeable improvement in a few weeks. Just because you can get fully carbed in 4 days doesn't necessarily mean the beer is ready to drink. It is a noticeable improvement.
Cheers.

 

In addition to what @billandsuz said, some more time in the keg will result in finer foam and better foam retention, probably due to CO2 hydration. So even though you can fast force carb your beer to X volumes of CO2, it's really not yet at its best foam-wise.