I have an '05 FLHRSI and have been looking at the Wild One 513's. I recently bought a Sundowner seat (from a forum member) and love it. BTW I'm 5'9".
As has been said, the seat/bar combination is the way to start. If you think you may change your seat, do it prior to getting new bars.

 

I'd change the fluids, in all 3 holes, and the brake fluid while I was at it.....
Tires are a "no-brainer" for me.... dump those old tires...... the price of good rubber, is worth my skin.....
You didn't mention what experience you have.....if you have any... you likely know what seats you like, and which direction you'll head in... do the seat FIRST.... then worry about the bars
What works for ME..... is the lift the bike off the sidestand, and then close my eyes, I raise my hands into what I feel is a natural position, and then I can measure, the distance between my hands, and the bars.

Fuel guage? they are rarely accurate, so I use the trip odometer.... even thoght my bike has on on the inner fairing.

 

And don't forget to flush your brake system as well. Folks tend to overlook that item.

In fact, it might be a good idea to have the dealer do the equivalent of the 10K service on the bike. That is a "tooth to tail" service that includes inspections, adjustments, and fluid changes.

Peace of mind on a new purchase, particularly for a bike that has been a garage queen for awhile, can be important.

 

Congrats on your purchase. I would keep an eye out for leaks springing up, seals that are sitting and not sealing will go bad, just my .02 . Stay safe and keep the shiney side up.