Capreso Infinity def doesn't grind fine enough or more importantly consistantly enough for machines like the Silvia etc. Had one before, it's fine for everything non-espresso. Its fine for espresso machines which have pressurized portafilters (which is where you'll see people saying it works for espresso). With the infinity adjustment you don't really have any play to tune espresso, you either sorta get close or too coarse. Especially as the beans age or different beans in general needing different settings, the 3 last espresso blends I used on my Preciso all have different settings, if I had the Infinity I sorta would have been screwed, could get shots, just won't taste good. Say you need "D" for a bean, one click either direction may give you "B" and "G", make sense? Cheapest new auto grinder for espresso would be the Breville Smart Grinder at around 200 or 20% off if you get a coupon for bed bath beyond. It can grind fine enough, pretty consistant, and more adjustment for eapresso over the infinity.Otherwise hand grinder is your best bet and cheap. You should save more though and find a good used machine.
You can see reviews here pretty much all pointing out its great for non-espresso needs, and similar reviews elsewhere online.
CoffeeGeek - Capresso Infinity GrinderHow did you acquire the Silvia? B/c new or used it's a pricey machine so just curious how you got it but can't afford/budget for a grinder? Unfortunately it's also one of the most picky/finicky machines around. Even if you get a good grinder you still have to learn temp surfing on it or it's pointless as you'll get extremely bitter or sour shots. The one bad part of the espresso hobby, is grinder capability, need a good adjustable grinder. You can have a $5,000 machine paired with a $100 grinder, but a $100 machine paired with a $300 grinder will far outperform it, it's all about the grinder. Couple hand grinders under 100 that will outperform the Infinity easily and comparable to grinders around the 200 range.
If you can stretch your budget to 250 (pry can even negotiate) there's a Preciso for sale on CG which you cannot beat for the money, I love mine, it compares to grinders costing twice as much for consistency and fineness, and control (macro and micro adjustment to dial your shots in).
CoffeeGeek - Members: Buy, Sell and Trade, FS: Baratza Virtuoso Preciso, like new, about 3 months old.