What type of grease should I buy specifically to prevent the seat post from getting stuck in the seat tube? I believe its aluminum. Is there all-purpose grease that I can use for other parts of the bike? This is an older, inexpensive bike that I need to last for another few years.
Carbon paste (AKA Carbon Prep) would be better than grease.
Its designed to provide grip so carbon components don't have to be over tightened, and is designed to work with metal on carbon and protect against galvanic corrosion. Exactly what is needed to stop a metal seat post sticking in metal frame.
Another thing that will prevent seizing is regular (monthly or 6 monthly depending on riding conditions) loosen the seat, give it a twist and tighten it up.
The only time that there's really only one right answer is if the frame and seatpost are dissimilar metals (aluminum/steel, titanium/aluminum, titanium/steel). In this scenario, you should ABSOLUTELY use an anti-seize compound. Something like Park's ASC-1 is perfect for this. The anti-seize compound has zinc in it, which acts as a sacrificial metal to prevent the frame and seatpost from corroding and bonding to each other.
For other materials, you can still use anti-sieze compound, but you don't need to. A thin layer of grease will work in most cases. In the event that you're having problems with a seatpost slipping even when clamped, then go with an anti-slip compound, like Park's SAC-2.