What kind of wattage for soldering small electronics?
A 30-40 watt fixed-temperature iron will be on the hot side for electronics work. It will melt solder very quickly and make it really easy to heat up large component leads quickly, such as those on connectors. However, it also risks exceeding the heat limits on more delicate components. If you have good technique so that you can make a joint quickly, you avoid the risk and get the benefit, but by the same token, I don't know that I would recommend an iron that hot to a newbie.
If you only want a simple pencil iron and are going to be using it primarily for relatively delicate parts — ICs, small-signal transistors, film capacitors... — you may want to start with something more in the 15 to 25 W range. Again, the hotter it is, the faster it is to make the joint, but also the quicker it can damage something.
There's a tradeoff, where the iron is too cool to heat the component lead and solder quickly so you also burn the board because it simply takes too long to make the joint. Some may argue that 15 W is below this limit, others may say it's just above the limit. I haven't used an iron that cool in so long that I couldn't really say.
The high road is to avoid all this and get a good temperature-controlled iron. With such a tool, you can trust that when you set the iron to 300°C to solder a component whose datasheet says it should be soldered at no more than 300°C for 5 seconds, that it won't die if you complete the joint in less than 5 seconds. With a fixed-temperature iron, you not only probably won't know the idle temp of the iron, you won't know how far its temp dips when loaded or how long it takes to recover. With a cheap adjustable iron, it probably won't be properly calibrated to give the rated temp at the tip with every combination of tip type, and you also get the "loading and recovery" problem.
I know you say you don't want a "super expensive" iron, but the one you pointed to is downright cheap, relatively speaking. It may be that it's a poor clone of the famous Hakko 936, and its bad value is signalled by being in that no-mans land between a basic pencil iron and the low-end of good temp-controlled irons. (I'd put that low end border at around $90 US, by the way.) It may also be that it's an outstanding value. I couldn't say, having not used it. Its price does make me wary, however, as does the fact that it's cloning a well-known design. Some clones are nearly as good as the original, a rare few are better, but most are worse. If you buy it, I'd say you'd want to be prepared to replace it.
Actually, for someone in that position, I'd say start with a $9 pencil iron and then later step up to a good temperature-controlled iron and skip over the no-mans land of cheapies you're looking at now.
As for "Weller" as a brand, they have a good reputation, but I've never used one, having never found one with the combination of features and price that made me happy. I've only ever used one name-brand iron, and it's way outside your price range. Everything else I've used successfully has been no-name house brand stuff. The point is that while quality matters, brand names aren't the best way to find it in this particular market. I suppose that's due to the fact that soldering irons are fundamentally not that complicated, and they're used worldwide, including in the same cheap Chinese factories we all love/hate. The poor Chinese laborer needs good irons, too, so they make their way out to the rest of us.
Get a soldering iron with a thermostat. This is much more important than the wattage. Without a good temperature control, you run the risk of putting too much heat into the PCB and damaging it (or the chips). It's easy enough to do that with temp control, but without it you're really at a disadvantage. Once you have a good temperature control, then something in the 20 to 50 watt range is good. If for some reason you can't get good temp control then stick with an iron that is less than 25 watts.
The soldering iron I use at my office is the Weller WESD51, and costs US$129 from Digikey. This thing will last 10-15 years. While that might sound expensive, it is well worth the money when you think of all the frustration it saves. It could even save you real money since you have less risk of damaging PCB's. Besides, $129 isn't a lot of money in the grand scheme of an electronics hobby that could easily cost 10x of that per year.