Let me revise my earlier statement about the cheapest setup for making real espresso:
I should have mentioned the Saeco Aroma (also known as Starbucks Barista, but not sold by Strarbucks anymore). This is really, really absolutely the cheapest machine you should buy if you want to make espresso. It is a proper pump/boiler machine. A thermoblock "15 bar" steam toy will never product anything other than strong (and bitter) coffee.
The Aroma is perfectly capable of making "espresso". However, if you want to make good espresso with it, ditch the pressurized portafilter for a $40 regular portafilter, and swap the frothing aid steam wand for a $22 Rancilio Silvia steam wand so you have a hope of making microfoam. You should also learn about temperature surfing a single boiler machine.
The Aroma seems to be going for $275-$350 now, so after you add the necessary parts to get the same functionality, the price isn't much different from the Lelit PL-041 I mentioned earlier as the cheapest machine to consider. The good news is that there a number of refurb black Aromas on eBay for $120-140. Spend $60 on some parts, and you have an espresso machine for only $180.
This machine must be paired with a good grinder. If you can afford to spend another $430, then please buy a Baratza Vario. I want to emphasize again how much more important the grinder is than the machine, once you have something at least capable of producing espresso. If you don't want to spend that much on a grinder right now, the best cheap grinder is a hand grinder. You can get a new Kyocera ceramic hand grinder for only $75. This is perfectly adequate for making espresso, and will outperform inexpensive electric grinders. The bad news: 200 cranks for a double. You've been meaning to work out, right?