Best money you can spend...most of us here have been at this for decades...if considering a new road bike purchase without a track record of previous bikes and related niggles due to less than ideal fit, is to consider a professional bike fitting.

Now, there are a couple of ways to do this. Inquire with the bike shop if they will give you a break on a pro fit...or, ask around at your local bike club and find out who the go to fitter is in town.

Fit is no.1 and even transcends your choice of bike. Fit is king and a pretty critical ingredient to your enjoyment on the road.

So, get a pro bike fit. If you are buying on line, you of course miss this vital step which many of us no longer need and we can buy a bike right to the nos. But you don't have this database in your hip pocket yet until you have owned a couple of bikes.

Good luck
PS: if you look at the chart...you will see reference to C to C versus C to T. These two references differ because of how a frame is measured. Center to Center is from center of crank to center of the top tube...even more complex is...with a sloped top tube is...'virtual sizing' as if the frame had a horizontal top tube. Center to Top is how frames are measured more conventionally...to top of top tube...again virtually if the bike doesn't have a horizontal top tube, and most don't today.

For you...your conventional bike size according to Dave Moulton who built this chart based upon thousands of fittings...you should be a a 48. A 46 is for the smallest among us...those in the 5' to 5'1-2" range. At 5'3" your sweet spot is closer to 48 C to T. That is a starting point and frames vary a bit mfr to mfr even within the convention of virtual seat tube sizing because of variance of of top tube length.

Your flexibility and even desire to ride aero affects your nominal position on the bike as well. So there is a lot to consider and no substitute for a fitter seeing you on the bike who will get a sense of your athleticism and even temperament for wanting to ride fast or more passive personality of just being out there on the road and smelling the flowers along the way. Some just want to hammer and their bike set up reflects this. Most don't however.