Kudos to your for making the big leap - dressage really is so much fun as there is ALWAYS more to learn, and believe it or not, any sound, reasonably well-conformed horse can make it to about Third Level with a good rider and correct training. (That translates to about Medium level in the UK, I believe.)
I like that you're not clutching at his head. A lot of aspiring dressage riders focus entirely on that lovely, round outline we see Moorlands Totilas et al. Trotting about in, but the part you need to be training is the rear-end. Roundness will come in time, and isn't necessary at the beginning levels anyway. The first thing to work on is forwardness - you want him happily moving off your leg at all three gaits, and slowing and halting off of your leg and seat. Experiment a little - you'll notice that when you get up in jumping position, he'll speed up, and when you sit back down he'll slow down. This is good, as it teaches you a powerful lesson about what you can do with your body, and it's the basis for everything to come. Work on adjusting your posting to what you want from him - in the beginning you'll want to post lightly (no butt-smacking) to encourage that big, forward stride. Later on, you can sit longer than you rise to help him shorten his stride, and when his back is educated and your seat is too, you can sit and make micro-adjustments via the motion of your hips.
He looks a little resistant to the bit and is turning to the outside. Have his teeth been checked lately? Make sure that's all in order, and then you can work on the education of his mouth (after you've got him forward-going and relaxed!). Your outside rein should be stable and steady - an ever familiar thing for him to rely on. Your inside rein can mimic that to an extent, but with 'gives' - second-long softenings of the rein to encourage and reward yielding, flexing, etc. At this point you can teach a basic half-halt - using the educated seat you will have attained, sit deeply for a stride as you would if you were asking for a down transition, squeeze slightly with your leg, and slightly pressurize the reins (no pulling!) - then GIVE. If you don't get any response, give anyway. The half-halt request should only last a stride - if you don't succeed, give and ask again. Make that your cardinal rule for everything!!
Once you've both learnt balance, go, stop, turn, all that fancy stuff, you need to address straightness. OK, well, ideally you should address this right after "go." Work on easy leg-yields, shoulder-ins, haunches-in, etc. With a green horse, it is preferable to get one good step of a movement than twenty iffy steps. Instead of turning down centre line and leg-yielding to the wall, turn down quarter line and ask for a step or two, straighten and go forward, ask for a step or two, etc. Same with shoulder-in, except on the wall of course. Start by riding an accurate ten-metre circle in the corner to get your horse in the correct position, and then proceed.
I also think that working with an instructor will help immensely. Learning dressage is kind of like memorizing an encyclopedia - you don't want to just dive in a do it all in one go. Having someone there to present everything to you in managable chunks is so much better than learning it all at home and then trying to remember while you ride! Good luck - I'm sure you'll have lots of fun! :)