Presumably the OP is in the US for having quoted the prices in USD. The Bianca in the USA costs USD 3k, The Elizabeth or the Rancilio at USD 1.7k and the Minima approx. 1.8k based on a quick internet search.
The Elizabeth is a great machine, very easy to maintain and use. It has the pre-infusion options, so that would give you some ability to “play” with certain coffees, which is nice.
However, it’s a “dead end” machine, in the sense you cannot really do much to it. It is what it is, and has to be used as intended. The same goes for the Rancilio.
The Minima would allow you to add a flow control valve to the E61, which can take you to the next level. As upgraditus knocks at my door (I have the Elizabeth), this is one of the things I would like to experiment with one day. For the moment, however, the Elizabeth has been performing rock solid for the past year and a half.
No idea about the Rancilio DB X. Looks like it’s a great machine, but it also feels like it’s a bolted-on experiment on their single boiler design. IMO, it’s early days and I wouldn’t touch it, specially given the fact that within one year, they already came up with an improved version, the “X”, and added a pressure gauge and pre-infusion option. Personally, I’d let it settle for another year at least.