It is slightly dependent on your *personal* definition of espresso. Also the choice depends on how easy you want its operation to be.

The [**moka pot**][1] is certainly the cheapest espresso-type device. However, it doesn't fall within the standards of a true Italian espresso, as pointed out in [this answer][2]. In particular, you won't have any crema.

[**Hand pumps**][7] are inexpensive, compact and light, and have the decent pressure of 8 bars. Although they are marketed as an espresso device for camping, they can be use wherever you have hot water.

A step up for home is an [**aeropress**][8]. The way it operates is steep + push-filter (as in a French press), and the result ranges from filter-brew-like to espresso-like.

Next in price are probably **the capsule espresso machines** (such as Nespresso and its clones), which many supermarket chains have cheap versions of. Very easy to use, but unsustainable (see [here][3] and in the end of [here][4]), and coffee enthusiasts won't consider them an option because of the taste (see the previous link). For related concerns, see the (excellent) answer to [this question][5].

And then come two best types: **bean-to-cup** and traditional **espresso machines** with a manually operated portafilter. They both are discussed in [this answer][6]. Both vary in price and quality significantly; probably a decent traditional machine may have a lower starting price than bean-to-cup machine. You may even find one not much more epensive than a capsule machine.

As far as easiness is concerned, capsule and bean-to-cup are obviously easier than moka pots or espresso machines.


  [1]: http://drinks.seriouseats.com/2011/06/how-to-use-a-moka-pot-stovetop-espresso-tips.html
  [2]: http://%20https://coffee.stackexchange.com/a/298/277
  [3]: https://sustainability.stackexchange.com/q/2501/2661
  [4]: https://www.choice.com.au/food-and-drink/drinks/tea-and-coffee/articles/coffee-capsules
  [5]: https://coffee.stackexchange.com/q/1572/277
  [6]: https://coffee.stackexchange.com/a/333/277
  [7]: http://www.wacaco.com/
  [8]: http://www.aerobie.com/product/aeropress/