Great question! I am going to use NY as an example as this is my home state. Early on members of the State Assembly would nominate candidates. Each party would caucus to nominate. So the Democrats would meet and nominate candidates and the Republicans in the immediate pre-Civil War and late nineteenth century (Whigs National Reps etc in earlier periods) would nominate their candidate. For example in the 1833 Senate election the Democrats, being the party in power, put forward 3 candidates, Nathaniel P. Tallmadge, New York Supreme Court Justice Jacob Sutherland, and Ex-Assemblyman Benjamin F. Butler while the Anti-Masons and National Republicans put forward Franics Granger. Eventually Tallmadge was elected once the Assembly vote and the NYS Senate voted. Now Tallmadge's election was controversial due to his eligibility, (I can discuss that if you want) Nevertheless he was re-elected in 1840 and remained a Senator until 1844.