I've heard that novelists often don't make good screenwriters and vice versa, but what if I wanted to try, rather than just try to get the novel published and sell the rights?
Would that be something to bring up *if* an agent expresses interest in my novel (and I know that's a big if, given how competitive publishing is)? Or would I try sending out the novel to literary agents and the screenplay to agents for screenwriters?
If someone expressed interest in one, would that help the other (e.g., if a literary agent expressed interest in the novel, then would that help in selling a screenplay or vice versa)?
Do you want to do the cover art too? Design the jacket?
Focus on writing a good novel. Then secure a literary agent.
Trying to secure an agent for a screenplay is next to impossible for someone not in the business.
You also don't want to just send your screenplay out to agents unsolicited. The rules on content control are much MUCH different in the film world than they are in publishing. You start sending your stuff out you're likely to see it at the local cineplex with no mention that you came up with that nifty idea of cowboys in space and shapeshifting.
One thing at a time.
And don't tell a literary agent you want to do the screenplay. It pegs you as a total amateur.
Film agents acquire rights to novels, they don't buy screenplays. They acquire rights, then attach people to the project. If you want to write the screenplay, you can certainly say so if the film rights are sold, but don't hold your breath.