A friend is purchasing a Rancilio Silvia for a home espresso machine. A reliable, time-tested prosumer machine with well-understood shortcomings (not much of a steam machine), which should serve her well. She's planning to put a PID thermostat on it from day one.
I've previously written about my multi-year experience with mine. That article doesn't have a shopping list for new owners; this one does.
The one thing that I'm not covering here is a grinder - she's going to have to sort that one out on her own. My broad recommendations involve perusing CraigsList or eBay for good deals on commercial espresso grinders, which will last a lifetime in home use. I've owned Mazzers mostly (I have a general purpose Ditting grinder too).
Beyond that, here's what I told her to get:
Tamper - I like Rattleware, the one that comes with the machine sucks. available on Amazon
Cleaning brush for group head - toothbrushes are the wrong shape. available on Amazon
Blind backet for backflushing - available on Amazon (see YouTube videos for espresso machine backflush). Rancilio says to not backflush the Silvia or you'll void their warranty. Ignore them. It won't hurt the machine unless you're a dumbass and leave it on for minutes at a time and burn out the pump. And even if you did, the pump is cheap (no, you don't need a spare, and I don't guarantee this is the exact model - check part numbers of course) - available on Amazon
But you do need some cleaning powder. I <3 Cafiza - available on Amazon -- also great for cleaning French Press bits.
Periodically you'll need to descale by running acidic water through the whole machine. The kind of acid matters - most people who want to do it on the cheap buy a pound of citric acid from the local organic foods bulk aisle. Don't use acetic acid (or vinegar, which is basically acetic acid). Or you can buy a can of the commercial stuff. You don't need to buy this today, but you will probably want to descale at six month or one year intervals. available on Amazon
You should keep a spare grouphead gasket on hand. They are a wear item, and last six months to a year before they start leaking, and they always seem to start at the most annoying time. My preferred method to get the old one out involves a drywall screw driven into the gasket with a shortie screwdriver, and a pair of pliers. The old one will come out in chunks; the reason it's not sealing is that it's old and brittle from the heat. available on Amazon
If you need stuff that's not available on Amazon or just plain prefer supporting smaller, more specialized merchants, I buy a lot of stuff from espressoparts.com - they stock pretty much everything you'd need to look after a Silvia.
The PID kit that I bought was from Auber Instruments
Oh, and lastly, Home Barista is great for resources and info.