Firstly, you don't need to start the game with an astro. You should expect to be able to win games without scoring a single astro (I remember having to do so to win a sc event, not fun).
Anyway your plan is to make money, and score out. You should expect that your opponent may get a good number of accesses on hq and r&d, and most of your ice should go there, unless you find a window to put an etr ice on the remote and can with some certainty put an agenda behind it without fear of losing it before next turn.
You don't need to hold onto pad campaigns etc just because you can't trigger the NEH ability that turn, more remotes means more stuff for the runner to check or keep track of. And of course if they don't run, seak out an agenda.
The most important stuff I have found is that you do need to ice centrals when you can, ideally etr on hq v criminals early, pop up or architect on R&D, but then more taxing ice on R&D as the game goes on. In the meantime you want to make a lot of money. And then you want to start scoring.
The beauty of the agenda suite is that 2/3s are easy to score out, but then you add sansans and biotics, and as long as you have a lot of money you can easily score agendas you'd never expect to be able to score if you have a sansan up and an astro token for example. Learning to maximise the use of your fast advance tools is half the battle.
Against clot, if you can score two agendas really early, then do it. If clot comes out and you are already on 4 or 5 points you should be fine. Just set up your ice and drip econ, purge, and lure out clot with assets that you play into your sansan server. At regionals there were a number of games where I sacrificed early hq and r&d accesses to score an astro on turn 2 behind etr ice on a remote against kate players, banking on slow starts.
Against Leela, play more ice. Stack an extra piece of ice or two on your servers, and also ice R&D (you should do this v a number of runners anyway).
Your success with the deck, as with many corp decks, will partly depend on you being able to read your opponent to understand when you might find unorthodox opportunities to score, and when you can risk 2 accesses on R&D which gives you a window to score something from HQ. You will almost always be racing, so a lot of games might end with 7-5 or 7-4 or 7-6 your way, but that's fine. That's as it should be