Hi smiff,
All tanks have to start somewhere and nothing good happens for free (financially or otherwsie).
Looks and appearance of a tank is somewhat a personal preference, particularly when it comes to things like the sides/back of the tank. Some folk let them go all 'natural', others, like myself, prefer the 'clean' look.
The 'overgrown' look is fine when you have plenty of corals and other stuff in the tank to take your eye off it, just look at 'Tims' tank, it looks great and you don't really notice the sides since the corals look so great, but on a tank like yours I think it would look 'cleaner' if you fitted a 'blue' background and cleaned off all the glass. How often you have to clean it will vary somewhat, I can get away with cleaning the back of my tank once every week or two, but the front gets a wipe over whenever I'm passing usually.
I use to let mine be 'natural', but once I started adding sps and I cleaned it I thought it made a huge improvement and would never go back.
If you are getting excessive algae growth, then that may indicate a nutrient issue that can be addressed separately.
What lighting do you have? It looks pretty 'white' which is fine, but I think in your tank , once you've cleaned it up, maybe a bit more 'blue' would help. Could you tuck your heater behind the rockwork? I'm guessing you don't have a sump, which would suggest that your budget would best suit a tank of 'softies'. Nothing wrong with that at all, they are easy/cheap to keep and a tank full of soft corals can look equally as good as a tank of sps corals. A well run 'softie' tank will always look better than a poorly run 'sps' tank.
Once you start adding some more corals it will give you something more to look at rather than rock and algae! Go easy on the fish, lots of fish result in lots of poo that needs lots of filtration to clean up.
My current tank started as a softie tank before I discovered the lure of sps a couple of years ago. Just to show you what time and effort results in, this is a VERY early picture of my tank, 6 or 7 years ago...
... and one from over a year ago...
As for naming your corals, hmm, bit tricky with the photos, but I'd guess the first could be an aiptasia (pest), the purple looks like a purple porities or could be re-tracted green star polpys which grown on a purple 'mat'.
Hope this helps
Chris