In the following sentence, which word should I use?
My favorite topics to talk about include politics and economy(or economics).
"Economy" is an amusing word.
If you say "the economy", it means all the production and consumption and buying and selling going on in the nation or the world or whatever scale is under discussion.
But if you just say "economy", it means frugality, that is, spending the minimum amount.
That is, if you say, "This class teaches economy", you mean, it teaches how to buy what you need for less money. But if you say, "This class teaches the economy", you mean it teaches about production and consumption and money. Note in that case we'd be more likely to say, "This class teaches about the economy."
"Economics" means the rules that govern how the economy works. Often we use "economics" and "the economy" as synonyms. The difference between the thing itself and how the thing works can be subtle.
They mean slightly different things:
In short, economy is treating the world as a marketplace and deals with the flow of money, while economics is the study of the world as a market. It also includes, all the factors which influence the flow of money.