Which kind of electric-assist bike would be appropriate?

The choice of whether to ride an electric-assist bike or regular bike involves a lot of different factors, including just your own personal wants and desires. E-bikes add an extra dimension to the riding that can make it more enjoyable for some, especially those that don't already have an affinity for bike riding to start with.

So any answer will necessarily involve a healthy dose of opinion, and you'll have to see which of those opinions seem to mirror your own approach to riding best.

That said, it's worth focusing on your specific scenario, as prep for your broader research into what electric bike specifically would work best for you…

IMHO an electric bike is most useful if you have one of a few different goals as a priority:

• Reducing time riding. Even on a flat, an electric bike will let an average cyclist go faster. Note however that an experienced, fit cyclist can easily ride at the same pace on flat terrain as a regular pedal-assist bike will operate (in the US, e-bikes treated as regular bikes are limited to 20 mph for assist, while outside the US, I believe the limit is 25 kph…faster than that, and the bikes become subject to at least some of the motor vehicle regulations, including prohibitions for use on bike/shared-use trails).
• Reduced effort. For some, this is as much about practicality as it is laziness. While an experienced, fit cyclist can maintain 20 mph on a flat, this still requires effort, which at the very least will likely involve sweating, and may call for specific clothing. With an e-bike, one can ride at higher speeds with relatively little effort, in street clothes and arrive at your destination ready to work, play, whatever.
• Flattening the hills. This is a corollary to the previous two points. In some locales, the riding is already very flat and comfortable, speed is not important (and may not be even possible, depending on congestion on the bike trails), and an e-bike would be superfluous. But in a hilly place, the presence of hills might significantly slow you down, and using an e-bike might turn an impractical ride (due to time or effort constraints) into a practical one.

As a case-in-point: I currently commute using an electric bike. I have for decades used a regular bike for commuting, but my longest ride had been about 10 miles, and for much of that time I was riding less than 5 miles each way. Even with moderate hills, this was fine for my level of fitness and time availability. But my commute has recently increased to about 25 miles, over very steep hills, amounting to about 1800 feet of vertical gain over the ride. Without an electric bike, this would probably be about 2.5 hours of riding each way, but with the electric bike, it's only 1.5 hours.

In your own example, the distance is clearly within the range I found comfortable on a regular bike, even with hills. So I'll point out the first obvious fact:

• While you may be getting tired now, you will find that over time, it gets easier. Probably a lot easier depending on your current fitness level. This depends a bit on how hilly it is, but even with hills you'll find you're able to climb them faster, or with less effort, or both. If you keep the travel time constant, you'll expend less effort as you get stronger. If you are willing to expend the same amount of perceived effort as you get stronger, you'll find that the ride goes more and more quickly. The bulk of the gains will come early in the process, and with such a short ride, you may not find much improvement after that, but the ride will stop feeling like a chore regardless.

In other words, don't judge the ride by how you feel now. I have found that a short 20-minute ride home after work is just what I need to unwind. One thing I've always valued about biking is that it's one of the few places I get any real exercise, and so I don't mind spending the time doing it. I quite enjoy it, actually. (That said, if your job involves a lot of heavy lifting or other exhausting work all day, maybe you'll never find biking home to be something you look forward to.)

On a ride of the length you're proposing, an electric bike is going to be more about transportation than fitness. Even without an electric motor, it's just barely long enough to improve your fitness, but with an electric motor, the ride will be shortened so much that even the aerobic benefit will be minimal, and you probably won't get much if any strength benefit.

If you do decide to get an electric bike, all of the information that's already out there should be all you need. That is, there are a myriad of choices, and most of them relate more to how the bike feels to you than the ride itself. Any electric bike you find would probably work fine on that commute.

That said…I did wind up forming my own opinions of electric bike configurations before I bought mine, through lots of test rides, so I'll share those:

• Most important: I really didn't like the bikes that didn't use torque sensors to govern the motor. Instead, they use pedal cadence sensors, and the motors are generally just "on" or "off". You can get used to that scheme, but I found that it made the bike seem more like an uncoordinated partner than part of the team. The motor would kick in hard immediately, instead of moderating its assist to match my pedal stroke, and it wasn't possible to smoothly adjust my speed with pedal force, because if I kept pedaling at all, the motor kept at its set boost. This gave the impression of the motor actually working harder as I pedaled more lightly and vice a versa, which is IMHO the opposite of what you want.
  
  So I strongly recommend considering only bikes that use a torque sensor to control the assist level.
• The other big configuration choice to look at is a hub-mounted motor vs a mid-drive motor. The former drives the wheel directly, the latter drives via the pedal crank. This is largely a subjective choice, partly driven by economics (the latter are generally more expensive). There are pros and cons to each, covered adequately by any number of other resources. The biggest differences come down to weight distribution (hub drive puts the weight rear-ward, which can affect bike handling more) and gearing (mid-drive takes advantage of the bike's gearing, and so can provide more torque over a wider range). IMHO, the weight distribution is the more important of these two, but this may only be an issue if you also tend to ride with a rear rack loaded down with gear (I do, but many people won't), and is in any case mitigated by the fact that the electric bikes tend to be significantly heavier than a regular bike, so the center of gravity (balance) of the bike doesn't actually shift that far rearward even with a heavy motor on the hub.

Other options mostly involve things like where the battery is mounted (again, rear-mounted batteries mess with the bike balance in ways that frame-mounted batteries don't), how big the battery is, whether it can be charged on or off the bike (but your short ride means this is probably not that important), manufacturer (I found that Brose, Yamaha, and Bosch systems all seemed to work better than the other manufacturers I found and tried, but this is far from an objective, educated observation), how much capacity the battery has (again, your short ride means that pretty much any e-bike should suffice), and of course all the other components on the bike.

Regarding components, mainly I mean the brand and quality level. But one other characteristic that could affect your choice is the drive-train. Specifically, internally-geared-hub vs derailleur (the former available only with mid-drive bikes, as far as I know), and if IGH, then whether the bike is belt-drive or chain-drive. I ride in all weather except heavy snow, so I opted for a belt-drive bike. But honestly, the best riding bike (in terms of just how the bike handled and fit me) I found was from Haibike, available only with a chain drive. It was really a difficult choice to make, but ultimately I knew I didn't want to spend all the extra time and mess dealing with cleaning the chain and gears after every ride in the rain.

If you only plan to ride in good weather, chain drive is great, costs significantly less, and is universally available (limiting yourself to belt drive means reducing the available options significantly).