I'll out myself as the second businessman
With your budget, you need the cash for a grinder and training.
A PID will remove the cooling flush with a Silvia but will not make you a superior coffee. Bottom line? You can't make coffee with steam. Wait until the Silvia comes to top of temperature and the heating light goes off. Flush the group until you hear no more steam as you make coffee with water, not steam. Shoot away and then do your milk.
All a PID will do is remove the cooling flush. I'd be spending the extra $$$ on the best grinder I could get and perhaps something like an Introduction to espresso course at the Angliss Coffee academy.
None of this will make me a cent and in fact will possibly lose me a sale. Regardless, I think it's the right advice. Buy the Silvia or a basic Lelit, get the best grinder you can afford and put the rest into training. I'd keep an eye peeled for a good pre-loved kit in the Hardware fo Sale Forum right here. You might save quite some $$$ by purchasing used. I would think that $600 should purchase a Silvia/Rocky combo here given that they're available at $950 new. The Compak K3P is better still and about the same price as a Rocky.
Good luck whichever way you decide to go!