I agree, a 16" midlength A3 is a nice starter upper, and makes for a really comfortable, ergonomic, and handy carbine. The current popular upper assembly is the 16" A3 with Carbine-length handguards and the reduced barrel diameter for the M203 grenade launcher for the M4 lookalike look, commonly called the "M4gery" pronounced M-forgery. Chances are you won't have a use for the M203 bracket cut, but some people think it's cool.
I have a similar flat top Bushmaster upper, with a 14.5" M203-cut barrel and permanently attached Izzy flash hider for the 16" minimum barrel length.
Whatever barrel you go with, be sure to get the 5.56 chamber, and either 1:7 or 1:9 twist so that it handles 55 gr and 62 gr bullets, the two that you'll likely end up shooting the most.
As to chrome bore /non-chrome bore, that's up to you. Chromium-plated bores tend to wear slower than non-plated bores but the chromium is said to detract from accuracy. Some people will say that chromium plating resists attack from corrosive ammo and that's true, but what 223 ammo is corrosive? My uppers with plated bores shoot better than I can, and I cannot detect any practical difference between my uppers with plated and non-plated bores. Plating usually adds an extra $50 or so to the cost of an upper assembly.
Get a A2 carry handle, or use the $$$ to get a simple rear BUIS like the YHM Rear Flip Sight or the MI A2 Rear Sight. Both have easy windage adjustments. These will cost between $75 and $100. Just this past weekend I bought another YHM Flip Rear for $80, and a MI A2 Rear for $75 for two of my uppers. Both the YHM and MI rear sights have spring-loaded detent buttons that lock them in the deployed, upright position. I've gotten great service from both for a while now.
There may be some ueber-tactical brand-conscious mall ninja types coming by later that will recommend a more expensive BUIS like the Troy or ARMS 40L. Both are great sights also. IMO a 1st time noob doesn't need to spend the $$$ just to brag they have the ultra-cool model popular with the brand-conscious crowd. The Troy is more expensive and does the same job as the YHM and MI units, and the ARMS has a little C-shaped keeper hook that I personally find off-putting.
JMO and experience, best of luck with your build!
Noah