For some reason the quote function is not working today so I'll just direct copy and paste questions:
"Do you have any suggestions for machines, grinders and beans?"
What machine to recommend depends on where you are, as you will want a service location relatively nearby. That said, the Gaggia Classic is a solid machine. And paired with a rancilo rocky essentials grinder it has all the tools needed to make decent espresso. Cost for both will be ~$500-600. That is twice what a nespresso machine costs but it will make much better coffee and it will cost you much less in the long run.
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"Also what are the other three variables? Beans, grind, ..?"
The five factors for espresso are brew temp, brew pressure, grind size and consistency, dosing factors (quantity of coffee, its distribution, tamp pressure) and brew time. Some consider dosing factors to be more than one variable, but I lump them all together.
Grind size and consistency is the hardest variable to control and has a huge impact on flavor profile - which is why a good grinder is important. A $700 grinder will make a crappy espresso machine much better, simply because the grind size will be far more consistent.
FWIW, I have an Expobar Office Lever (with a PID mod for brew temp) and a Baratzo Vario Grinder. The total cost of the package was about $1800, which is a lot of money but not anywhere near as much as what you can spend. I committed to that level of equipment because I wanted it to be very durable and capable of producing a very high quality shot every time I use it. I also calculated that based on what I was spending on coffee at coffee shops, the machine would pay for itself in about 8 months.