Of the canon named characters I'm most interested in Boromir (to complete the fellowship, minus the hobbits) and Radagast.
Boromir might be on the young side to fit the 'between the Hobbit and Fellowship' timeframe, but I think it works. He was 23 at the start of the Fellowship (and he was 40 when the Fellowship was formed). He might have been adventuring since he was 16. We know he was a great warrior and captain that fought Orcs in Gondor before joining the fellowship.
Outside of Boromir and Radagast we're sorely missing people from Rohan and I'd like a Beorning. I also wouldn't mind another hobbit. But for these categories I care less if they are canon or not.