Does running a lightning node support the network?

I finally took the plunge and puchased a raspberry pi with the intention of creating my own bitcoin node. I have been doing some research and hoping for some quick answers here. (Sorry, lazy I know).

1. I can run a bitcoin (core) node or a bitcoin lightening node. Correct?
2. I see that running a bitcoin node does not necessarily produce any profit. However a lightning node is (potentially) profitable. Correct?
3. Does running a lightning node support the bitcoin network in the same way a bitcoin core node would?

Please forgive any ignorance here. I am in the beginning stages. While profit sounds wonderful, I am also interested in supporting the networks decentralization. It would be a hard choice between the two for me.

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I appreciate any feedback!