Keep in mind, your decision will ripple through the other two prequel movies, so choose wisely.
It would be best if you also extrapolated on how you expect your decision to affect episodes 2 and 3.
Do you:
1. Remove Jar-Jar?
2. Change Anakin from a whiny kid to a damaged 13 year old slave boy (thereby closely matching Padme's age)?
3. Allow Darth Maul to survive?
Choose your destiny.
I would have had both Anakin and Padme be older, maybe around 16 or 18.
Also, instead of Padme being an "elected Monarch" she can just be a regular Monarch. I know it didn't seem PC to have a royal family and ruler, but I think the audience would have forgiven it (no one ever had a problem with Princess Leia). Maybe her father, who was a wise and popular king, had suddenly died recently, and she was new and inexperienced at being in power. The Trade Federation would be trying to take advantage of that and her own people would have their doubts about her. When she prevails in the end and Naboo wins the war, she's lauded for her bravery and is immensely popular with her people. After 7 or 8 years she feels burned out from ruling and steps down, looking to get away from public life for awhile, and her younger sister takes over. But the Senator who replaced Papaltine mysteriously dies, and the people rally for her to take over in the Senate. So her sister appoints her to the vacate seat, refusing Padme's request to retire.
Or you can just have a 14 year old be elected Queen, with term limits. And then she is succeeded by another 14 year old.
1. Jar Jar name change to something less dumb, and rewritten as not clumsy, not dumb, and not a pathetic lifeform.
2. Anakin discovered at 13 years old on Tatooine, Anakin did not build or create C-3PO.
3. No Pod Race. Republic credits are converted to Tatooine Outer-Rim Currency at the nearby ATM, Hyperdrive Generator re-labeled as KDY-Type 101 instead of Noobian. Qwi-Gon finds out about Anakin's extremely mechanical intelligence level and wants to buy him. However, Qwi-Gon only has enough credits along for Anakin Skywalker. He says he will return to buy Shmi.
4. Tatooine is no longer in the Naboo System and is an Outer-Rim World as revealed in the Original Trilogy.
5. Jabba the Hutt more closely resembles his Return of the Jedi self. Other Return of the Jedi favorites are with him, including the Gamorean Guards and Twi'Lek Dancers to keep company.
6. Darth Maul does not die to the Jedi, instead escapes from Naboo and rejoins Darth Sidious who, from his point of view, executes him for running away from the fight.
7. Count Dooku name change to purely Darth Tyrannus, steps from the shadows and joins Sidious at the end of the movie. He was also never Qwi-Gon Jinn's Jedi master.
8. Reactor Core not in the hangar bay of the Trade Federation Ship, instead, Anakin uses his intelligence of building things on Tatooine to determine the weakest point of the Trade Federation Ship and instructs the other Naboo pilots to attack there.
9. It is revealed as to why the Trade Federation trusts Darth Sidious, and how they became in league with him.
10. After the movie, during a post-credits scene, Anakin, Obi-Wan, Padme Amidala, C3PO, R2D2, and Chancellor Palpatine and his advisors, return to Tatooine and buy Shmi Skywalker from Watto. Shmi goes with Anakin, Obi-Wan, and Palpatine to Coruscant where she can watch Anakin train as as Jedi Knight. Shmi Skywalker falls in love with Palpatine and so it is finally revealed as to who Rey's Grandmother is.
Out of those choices, I think number 2 would be best. Jar-Jar is bad comic relief, Darth Maul is a dopey lieutenant of evil type of character and doesn't need to survive.
The prequels were a character study of a good man who turns evil. That they failed was because Lucas failed to write an interesting or top-notch character arc. Giving Anakin a better starting place could have snowballed into a more satisfying arc.
But I don't think any or all of these would change prequel history. I think Lucas bungled just about every aspect of the prequels, so I think you'd have to gut them and overhaul them almost completely to make them work - if that's even possible.
At its core, I think the original films gave a full and complete character arc for their main character - Luke. For a long time now I've felt that one of the problems with putting films before and after is that Star Wars was always kinda Luke's story. When he's not there, the saga lacks direction and focus.