Love to hit up Monaco too, but I have no idea if that's feasible on a budget.
Monaco is easily doable on a budget. Your budget is five figures, right?
No, seriously. Monaco you're looking at stupid figures. While there are some cheaper tickets, you basically have to buy a grandstand ticket to see anything as it's not like Melbourne where there's general admin areas with a view of the circuit. There's a few ~100 tickets with distance from afar (sorta like going to the Gold Coast and renting an apartment over the other side of the road), but most are around EUR400 per person.
While I haven't done it myself, I'm told accomodation in Monaco during the Grand Prix (and Cannes - remember, Monaco is done around the film festival) is crazy - I've heard of people staying as far away as Marseiles and catching a train there each day, from memory. Most have to stay in Nice.