Ok, I'm confused. How many fish?

Tall tanks are kind of bad in that way. They just don't offer as much surface area as you have noted. Obviously they can hold more fish than a 10 gallon tank but still they cannot hold as much as a 20 gallon long tank.

Do you have some sort of stocking scheme in mind? Are you looking for small bodied tetras etc... or something a little on the bigger side?

Tall tanks are kind of bad in that way. They just don't offer as much surface area as you have noted.

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I agree, except that I would say tall tanks are good in that way. you get more water volume per fish, and therefore a more stable environment, and happier fish. I am one of a very few fans of tall tanks, however I Personally wouldn't put many more fish in my 115 than most people would put in a 75 because the surface area is the same. I like the look and stability of the 115 far better than the 75g though. my fish get more water for the floor space.

The fish per gallon rules and the fish per square inch rules are realy borderline on useless, I do use these rules of thumb as a starting point for planning, but if they aren't combined with a few years of experience thay just don't fly. Let us know some of your ideas for what you want to own, and we can help. Also stocking levels rely greatly on filtration, I might tend to crowd a 75 with 1200 gph of flow through good bio and mechanicle filtration, but would lightly stock a 20 high with one AC 150 on it. Just my thoughts.

At the moment the bioload isn't too bad. But that filter is borderline at best for that size tank. A general rule of thumb (here we go again) for fresh water tanks is to look for a minimum of 5-6 times water exchange per hour. So in a 20 gallon tank you would want to use a filter that could produce 100-120 gph of flow. You can easily get away with smaller filters but take that into account when thinking of stocking. Those neons don't produce a ton of waste but if dropped in a pleco then you might be in trouble.

minimum of 5-6 times water exchange per hour

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Fully agreed, key word being minimum,
Filter ratings are like fish per inch rules IMO. they give you a ballpark but nothing sound. I personally would have 180-240 gph on this tank ( tend to go as high as I can on filtration), The only time you have to worry is if you have fish which don't like current, and there are ways around that as well. I learned to be a filtration fanatic the hard way (with Oscars), with fish that grow big like angels, everything will go fine and then one day as the fish grow, the tank will start giving you trouble, and keep getting worse. you will either end up doing way more maintnance than I think is fun, or you will have unhappy fish. I personally would buy another filter of about the same size and add it. other than the filter cost this won't really increase your cost a lot because the dirt load in the media will be divided, and therefore it will last twice as long. There will be a very nominal increase in electrical use but I find it irrelevant.

Most HOB (hang on back) filters are great at biological filtration. In other words they get out the ammonia, nitrite etc... by making a place for the good bacteria to live in large numbers. Canister filters tend to be better at mechanical filtration (as well as biological). So a small canister filter could be a good way to go. Something liek the fluval 104 or something. Plus if one filter breaks then you still have the second to keep the tank happy. I always suggest that tanks have 2 filter when they start to get bigger. 20 gallons isn't super big , but it also depends on the fish load.

One other thing when looking at the number of fish, is the activity of the species and what size territory they might need. If you have some zippy fish like Danios, you need more space for them to move around in. Or if you have territorial fish, you'll need to give them the room and cover for their territories or you can have some really nasty fights ending in severe injury or death.
My suggestion: research, reasearch, rreasearch. Sites like this are the best, because you can take advantage of years of experience and different points of view. If some one forgets something, it's a good bet that someone else will cover it.

Would you have any advice for a different filter to add to my tank?

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As your tank is already set up, a rfug system is out. I personally would go with an AC (aqua clear) filter, they are very simple, reasonably dependable, and are basically a large media well that allows many choices. Stuff it full of sponges, skip the carbon unless there is a specific need. If you want to get real fancy, buy a reverse flow sponge kit and put it on the intake for prefiltering. I also like emporer's, they are my primary filter on most large tanks that I have ever set up. on smaller tanks I usually use AC mini's and 150's. I have also used some wispers, and can't say that I've had trouble, but for some reason I personally don't like them that well.