The UH30301 is the best one by far. It is simple, but gets the job done. The brush roll shutoff is nice for hard floors, the HEPA bags are clean to maintain and filter well, the machine itself is fairly lightweight, and so forth.
The UH72625 does not arrive as pictured. They removed the brush roll shutoff, so it is bad for hard floors. The UH30301 still has the brush roll shutoff, so it is the better choice. They also removed the changeover knob for the hose, which was a huge downgrade to the performance of the unit. With the removal of those features, they also removed the build quality almost entirely. Overall, the UH30301 is just better.
The UH74220PC is not terrible, but it is a tad expensive for the build quality that is received. They are somewhat notorious for the clip in the handle breaking, for example. For that reason, I do not normally suggest it or similar Hoovers unless they are super on sale.
If you really want a swiveling bagless upright unit, the HART version of the same basic unit is around half the price and a far superior deal. HART is a brand from the same company that owns the Hoover brand, so it is the real thing and not a knockoff as some folks assume.
If you want something similar in price to the UH74220PC but a better bang for your buck, the Kenmore DU3017 is a way better choice with better build quality, excellent cyclones, a lift-away mode, and onward. I would argue that this one is a better vacuum cleaner than even the UH30301. It has more features and I have found them to be more durable through regular use.
I am not sure of your maximum budget, but I would personally go for the Kenmore CrossOver over the Shark or Dyson. Not only is it a brand new unit instead of a refurbished one, it has a far better cyclonic bin than the Shark and a vastly superior head design to the Dyson Ball models other than the Ball Animal 3, among other things.
Between the Shark and the Dyson, I prefer the Dyson models. They tend to be a little more reliable and have the superior bin design that requires a lot less filter care. Just make sure you keep the roller clean along with other regular maintenance. If you can get your hands on a Ball Animal 3, I would suggest it over the older variants due to the improved head design, but I suggest the Ball Animal Pro or Ball Animal 2 over the Shark Vertex for sure.
That is a new version of one of the earlier successful Shark models. While it's not an awful deal at $119, there are definitely better deals out there. The main drawback of that Shark is the build quality (though it's probably good enough for $119) and mostly the cyclone/filtration setup. The exhaust filtration is quite decent, but the dust bin has only a single cyclone and huge foam filters that get dirty basically instantly due to the primitive single cyclone, making them a hassle to clean (and you'll be doing it often).
You could check out the Hart Pro Bagless Upright for a wildly cheap $69. This is a Wal-Mart special, but Hart is a TTI brand so it basically is a shared design with Hoover. You do lose the lift-away feature with this, but it is significantly cheaper and has likely a similar build quality. You also get a dual cyclone with this model.
If you really like the lift-away feature, the Kenmore CrossOver is a little more at $209, but has all the features of both as well as a rather solid build for the price.