Northern Italy 10 day itinerary

Why not pick up rental car AFTER seeing Florence, rather then before and having to park it?

You can rent a car in Florence at/near the station or at the airport. Tertium non datur.

I use www.autoeurope.com for my rental needs.

A rental car may be useful for lake Garda but totally useless to visit Verona or Venice.

My feeling is that you are trying to do too much. Three nights equals two full days. Your itinerary has too much traveling and not enough "being" and soaking in the charms of each location.
In addition, you're really late for reserving accommodations for this May. I'd encourage you to firm up your itinerary asap, once you've trimmed the schedule a bit.
Doing Venice as a day trip is a disservice to this unique city, and I doubt you would enjoy it. You need to experience the mornings and evenings on the canals, relax, and wander.
The Bernina Express route is fantastic. We used the regional trains, on the exact same tracks as the panoramic trains. You may be too late anyhow for a reservation on the panoramic trains, which is no real loss. The regional trains are not crowded and very pleasant.
In any case, whatever you plan, have a great trip and safe travels.

We were thinking of renting the car in the morning due to having our luggage..not too sure if we’d want to walk around with them. That’s my problem, I want to see everything! It’s making it hard to narrow down. Thanks for the advice! Might stay a night in Venice, thanks for the tip.

It's really not a good idea to store luggage in a parked car. Sorry. Many train stations have luggage lockers for storage.

I only can answer about Lake Garda:
4 nights there are only 3 days. If you want to explore the lake you'd need these days on the lake. But don't stay in Peschiera, much bettter go by bus to Garda Town. There you have the best connection around the lake by ferry and by bus, also to the northern part of the Lake (Malcesine or Riva).
Venice is not a good idea out of any town around Lake Garda, it is too far away for a daytrip. But Verona is easily done out of Garda Town by public bus.
And overall: you don't need a car on the lake. just the opposite, it only would be a hindrance. you'd have problems finding a parking space. So much better using busses and ferries.
But as you want to come in May, you should book your accommodation there ASAP. Good rooms are fully booked far in advance.
If you have more questions about the lake, don't hesitate to ask.

Thank you for the advice about the luggage in Florence, will look into that.

As for Lake Garda, have you been to Cascate del Varone? Is it worht it? What about Santuario Basilica Madonna della Corona, what's the best way to get there without a car? We would be open to a tour that picks us up.

This trip is for our honeymoon, we are both under 30 and like to hike but also want to spend some time relaxing around the lake. Any suggestions on where we should visit around the lake?

Lake Garda is not served by rail except for Peschiera or Desenzano. A car may be useful to visit more efficiently certain places of lake Garda (like some towns on the north side, Strada della Forra, Tremosine, Santuario della Madonna della Corona). You can reach those places through other means, but not as efficiently and fast. Parking would not be an issue anywhere, except for Sirmione if you go on a weekend. I've driven there in July more than once (and July is the busiest time) and there are ample parking lots options in virtually every town.

However you have very little time on the lake (at Peschiera), therefore you'd have time to see only Sirmione and some other place with a ferry. You basically seem that you intend to use Peschiera as a base to see Verona and Venice, places for which a car would be useless.

If you intended to stay at the lake for 4 nights (which is basically 3 days), to just see the lake, then a car might make sense, especially if you intend to see the Santuario della Madonna della Corona (very cumbersome to reach without a car), Tremosine and the Strada della Forra (which however I don't know if it has been reopened after the landslide). But if out of the 3 days, you plan to spend a full day in Verona and another full day in Venice (both of which should be reached by train), then all you have left for the lake is a day, which is probably enough only to see Sirmione (the main destination on the south side) and at most another town (but not too far north because you don't have the time with less than a day left after Sirmione and the lake is very long) which you can reach by ferry or bus.

No, a car around Lake Garda is only a hindrance. Roads are crammed and parking space are rare and expensive. Much better:
stay midlake area, Bardolino or Garda town. From there you can visit all around the lake by ferry or bus.
For cascada del Varone you could go by bus or ferry to Riva and then walk (I think there is a bus to the cascada also, but I'm not sure). If you have a day of it would be a nice experience.
But if the weather is fine I would recommend taking the bus (early in the morning!!!) to Malcesine and then go up to Monte Baldo by cable car.
Sanctuario Madonna della Corona is a bit more difficult. There are busses to Spiazzi out of Garda Town, you have to change in Caprino Veronese. And from Spiazzi you have to walk down to the Sanctuario. Only in high season there are shuttles down.
As I wrote above: Staying in Peschiera is a bad decision if you want to see the northern Part of the lake. And to add: Sirmione is the most crowded and the most overrated village around the lake. I only can imagine it is about they do a very good advertising.

Thank you both for your advice! I think since we don't have much time there we will need to decide what we want to see most. Going to try to book an AirBnb today, wish me luck!