I would think that any lingering neck issues should be the first thing on the list to address. Range of motion issues? Pain? Issues with vibrations or pounding, holding your head UP while riding a road bike with 'drop bars'?

Some bikes are designed with a nod to more comfort, with a taller head tube (the tube the front fork attaches to) which puts the bars in a higher position, and tube types/shapes that are geared for compliance and shock dissipation. 'Racers' like a stiff frame to transmit all their movements into forward motion but those stiff frames can ride harsh.

Aluminum bikes tend to transmit road vibrations and ride 'harsher' than carbon fiber but cost less. The Specialized Dolce Comp and Elite have 'zertz' vibration dampeners in the fork and frame that can take a bit of the edge off that but if you can get carbon fiber into your budget it would be even better. Looking for last year's model (often times just a color change or small change to components) can net you some savings, but it's tough finding dealers with small bikes to begin with.

I'm 5'1 with 27.5" inseam and rode a 48cm Ruby but found the 44cm a much better fit. If you can, find a dealer with small bikes in stock to try out. I had to go to a number of dealers just to find one bike to try. It can be frustrating.

As was stated already, the stiffer the better for shoes. You may want to go with flat pedals or clipless 'SPD' (mountain bike type) pedals and use MTB shoes if you want walk-ability. 'Road' shoes aren't very easy to walk in. As for shorts and shirts, I always wait for sales and found a few brands I like and stick with. Helmets- get one that fits properly, they all have to meet the same safety standards. You get a helmet with better air venting (usually) and lighter weight as the price goes up.

Then the little bits. Multitool, tire 'irons' (to remove the tire), a couple spare tubes, seat bag, on-the-bike pump, floor pump. Get a few tube 'repair kits' and have the LBS show you how to patch a tube (don't get the pre-glued patches, they suck, get the patch kit with the tube of glue and sandpaper). It's best to learn before you have a flat, how to remove the tube, find the hole, patch and remount the tire and inflate and put it back on the bike. Beats sitting on the side of the road, waiting for a sag wagon.