Cheap Espresso Machine
Is there any cheap espresso machine that would produce a good espresso? "True espresso" is produced by brewing coffee under pressure of at least 8 bars. So, if you want to make "true espresso" you need either piston driven or pump driven espresso machine. These machines are not cheap. In general, it is a good idea to budget at least $300 for a good pump espresso machine. If you are on a tight budget, there are some cheap pump espresso machines around but they are not without problems. I discuss several models under $100 in my article about inexpensive espresso machines.
Alternatives to home espresso machines
If you are not a purist, you may think about espresso simply as about coffee that is brewed under pressure. Historically it is correct. The first machine capable of producing true espresso came in 1940's. Before that espresso was produced by steam pressure.
To satisfy the purists lets call the beverage produced by steam pressure alone an "espresso-style coffee". There are two ways to produce this "espresso-style coffee" and neither of them will break your bank.
A Moka pot is a stovetop espresso maker very popular in Italy. They are very cheap (you can easily get one for under $20) and they make very good espresso-style coffee. There is usually no crema. The only Moka pot that produces a crema and that in general comes closest to making true espresso is Bialetti Brikka.
Now what about making latte or cappuccino with a Moka pot? Well, it can be done. You have two options in here. Either you can get a manual milk frother they are really simple to use. Or you can get Mukka Express which is a cappuccino maker from Bialetti.
You can read about Brikka, Mukka Express and other cheap espresso makers in more details.
Steam espresso machines
The steam espresso makers use steam pressure to force the water through the coffee. They are usually less than $100. These inexpensive espresso machines are a good bet if you drink mainly milk based drinks like cappuccino or latte. They come with a steam wand for frothing your milk which is really convenient.
If you are after straight espresso I would not recommend you to buy one of these. Get a Moka pot instead - it is not only cheaper but it is also likely to produce better coffee. In addition they do not break so easily. If you are attracted by the convenience of the steam espresso machines then you may want to consider getting an electric Moka pot.
Further ReadingInexpensive Espresso Machines
Espresso Machine Types
Types of Stovetop Espresso Pots
Electric Moka Pots