Yes to the balcony. On a 3000-passenger ship, it's going to be your only private outdoor space. Consider whether you want the shady or sunny side of the ship.
Our favorites are Celebrity and Princess. RCI was great too, but we last sailed with them in 2009; we had enough cruise nights to get Elite on Celebrity, and they're a little more upscale. Norwegian has some good dining, but since last year you cannot bring on ANY beverage, not even water, at embarkation or any port. That killed OUR golden goose for sure. What cheapskates. Plus, their ships are tending to the larger side, and we think 2500-3000 is just plenty.
TA cruises are bargains, but unless you book them a year in advance, you're not going to get perks like free beverage package or Internet. You'll still save. You might if you book one onboard a previous cruise. You have to be the kind of cruiser that likes sea days, as there'll be at least 6 or 7 of them.
We came eastbound in April 2017 on Celebrity Silhouette, and today we're westbound on Celebrity Reflection, somewhere between Rome and Barcelona. See you in November.
Oh, nowadays the internet is pretty darn good, but they've started selling it not by the minute but per-cruise. It's about $15-20 per day but there are discounts for loyalty club members. For us, 14 days is $220. As always, read cruisecritic.com forums for TUG-like insight.