You can buy a lot of armed militia to defend you for a trillion dollars. And who said anybody but me and the Chinese knew about this little deal?
Okay, fine, I’ll be serious. Am I the president now or in some hypothetical, happier time?
Seriously, I would devote it all to the objective of paying off the national debt. It would drop in there like a thimble into an empty bucket if the deficit’s anything like it is now, but every little bit helps. Maybe it would shore up the economy or curb inflation or something, and worst comes to worse, I can always grow the debt back again by spending, on multiple objectives.
Assuming the Chinese didn’t go for that… as to the options you list, it depends on what’s going on. Is the infrastructure really crumbling that badly? As in, public, government-owned infrastructure? Then I’d fix that. Otherwise not (obviously).
It’s not going to provide healthcare or education for any significant length of time unless you mean to use the money to bribe politicians to change policy. In that case, I would bribe myself as well - it’s only fair, right?
I wouldn’t bail anyone out unless I bought them out - by which I mean, socialized their industry. But in that case I’d probably need that money for bribes again…
I wouldn’t put it in the social security system - if I can stop the other politicians from pillaging it, then it’ll be fine; if I can’t, dumping another trillion in there would just give them more to ‘borrow’ from it.
Devoting it into researching and developing serious alternative energy options might be worthwhile. How many nuke plants can you buy for a trillion dollars? (Minus the bribes and community ‘donation’ payoffs against NIMBYism, I mean.)
I wouldn’t start any wars or send any manned spacecraft anywhere, unless the economy and all that was so good I couldn’t find anywhere else to put the money. In which case, sure, why not invade Mars? If we have the money to burn, that is.