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I was planning to get the battlebox already but what else should I start out with?

Battlebox is always a good place to start for learning the rules...but move up as soon as you can. They aren't always as balanced against each other as you'd want them to be.

You can stick with the battlebox for a while though. After that though, assuming you want to stick with Syntherion (and there's no reason not to honestly, he's very good at what he does), you can't go wrong with an Algorithm Dispersion Optifex for sticking Magnetic Hold and an Optifex Directive for generally making vectors awesome. I believe that takes you to 13 points so you can add in your choice of servitor squad to crank it to 15. I'm really not sure if that's the best path since you might want more vectors before you add in so many optifexen, but it's all stuff Syntherion likes.

Alternately Syntherion doesn't need a corollary as much as some other casters since he does nothing with his focus but allocate it all away (his spell list is all upkeeps he maintains for free), but having one around is literally never a bad choice, and is probably the most generically useful model you can buy for Convergence. Additionally if you want to play him tiered you need a corollary and get an absolutely ridiculous bonus for doing so...

Cool, thank you for the information. Now I know what to buy for right now.

While Colossals aren't required by any means, and they're certainly expensive, Syntherion loves his Prime Axiom. Synth's feat means that the PA can wreck some serious havoc on opponents by getting four PS20 attacks. If you get within melee distance of another Colossal you can wreck it easily in one turn, sometimes without having to buy attacks.