OP - I'm a number of years older than you and I think at your age you're still experimenting/developing your style. Well done for working on it.
I personally find T-shirts to be a pain in the arse insofar as their trends change
all the time. Having said that, you have heaps of cheap options at Zara, Topman, Asos and the like.
Have at least a couple of plain T-shirts on hand, in visually-pleasing colours such as green or violet-blue. Look for Henley shirts in addition to simple crew- or V-necks. I haven't tried this yet but band T-shirts can actually work for you
if it's not something that's a) done to death (i.e. Ramones, Johnny Cash) or b) hit-and-miss (Eminem, 1D). If it's something timeless (Pink Floyd) or indie (Sonic Youth) you'll get positive attention for it depending on the crowd you're trying to pull.
My T-shirt look these days is bit more minimalist but bold like cardguy's Zapatista design. My current favourite is a No Pasarán design:
I personally prefer button-down shirts over T-shirts for the above reason though unless I'm layering up. I like your denim shirt and again, aim for designs that set you apart and doesn't look like you got it from M&S.
Checks are all right
if they're smaller and a bit more minimal -- I prefer the gingham check myself. Also look for shirts with a very subtle stripe. Think hairline or pin stripes without too much contrast:
Fit is as essential as the actual pattern but that applies to all clothing.
Something that has been much overlooked on this thread is jumpers.
When you've gained a bit of bulk, go for plain, form-fitting knits like these:
Jacked, well-off guys tend to rock this look -- especially as a shallow V-neck and over a T-shirt.
With your build I'd go for something a bit more chunky though. Look for cardigans.
I'm probably going to get eaten alive for saying this but I've had a soft spot for hipster-y jumpers for some time. I'm referring to patchwork, Fair Isle or Aztec patterns like this:
I've gotten a number of compliments on campus wearing something like that so girls dig it. I know some of you might its gay but the trick is to wears patterns that aren't too busy and obviously don't wear them going out.
If it's really not your thing, stick to a more conservative pattern like an Argyll
with more of a contrast than the following:
With shoes, I'd look for something that grabs attention -- I have a pair of London Adidas shoes exactly like these:
And get a pair of solid boots for winter. Eventually you'll want a pair of slimmer, dressier ones and a pair that's chunkier, more casual. I especially like Chelsea boots because they're less busy. If you can happen a pair of R.M. Williams, get those. Depending on the colour, they're smart and you can wear them with quite literally anything.
You're on the right track with jeans. Echoing what the others have said about hard denim, I'd also consider different colours. Burgundy is something I've gotten into but not everyone can get away with them.
Experiment with chinos of different shades (my little brother has a pair in mustard) but only wear those in spring/summer.