I've had a lot of success with hang on tank filters. Also, sponge filters work great for biological filtration and are super cheap- they aren't as good for mechanical filtration, though. I do clean my filter sponge, but not the biological media (little ceramic noodle looking things)- that's where the beneficial bacteria live. Under gravel filters are ok but for me they're a pain- detritus builds up underneath them and is hard to get out- also, if you ever want to change it or remove it, you will have a hard time.
I found this video to be helpful- he also compares other types of filters as well- super informational.
Depending on the kind of algae there are suggestions out there for treating it with hydrogen peroxide and a syringe- I haven't done it, but have seen them around. Also, folks say that Flourish Excel will help get rid of beard algae.
This article on the Seachem website talks about what to do.
When I put my latest tank together, I was very impatient and could not stop myself from messing with it. I put tons of plants in, and used a
cheap kind of CO2 solution. With it, you have to be very diligent to keep it stable, and I was not. I would alternately blast the tank with CO2 and then nothing. Eventually, I started getting beard algae. I kept thinking it would go away- I tried all kinds of stuff, but to no avail.
Eventually, I had to remove all plants and hardscape and completely start again. This time I have gone slowly. I never completely got rid of the beard algae (it is super difficult to scrape off - it is still in a couple of corners and on a few bits of gravel I haven't managed to tweeze out yet), but you have to look hard to find it. I've done a bunch of reading between then and now and went much more slowly with the way I added plants and what I do to feed them.
Knock on wood it'll go better for me this time. I do water changes every other day or so- 2 - 4 gallons (15 gallon total). I also try to only feed the fish every other day because I think I probably over feed.
Good luck - for me it was heartbreaking to take it all down and start over, but it was worth it. Mine had just gotten too far to deal with as it was.