Classical/Orchestral/Opera recommendations

[caustic1200]

I came across a list on the NPR website a few weeks ago in which you may be interested. Although broad, it will give you an idea as to what you do and don't enjoy. Further, it recommends specific recordings by particular conductors - a nice addition as there are often an overwhelming number of choices.
http://www.npr.org/programs/pt/features/pt50.html

[BigBank_Hank]

As stated before you should try some of the more popular pieces. Start with some of Beethoven Symphonies: 3,5,7,9.

For piano try Fryderyk Chopin first. You could download the soundtrack to the pianist for some of the more famous pieces. Another great pianist is Sergey Rachmaninov very beautiful stuff my personal favorite is Piano Concerto No. 2 in C minor, Op. 18.

For Cello the one piece that you need in your collection is J.S. Bach The Complete Cello Suites by Yo Yo Ma. I probably listen to that each and every day.

That’s should be enough to keep you busy for quite a while.

[limesqueezer]

New Swing Quartet

[jwartak]

Without being too difficult, there is no "best" place to start in Classical music. If you want to try the traditional way, don't try anything 20th century cause it'll be too influenced by other styles. 19th century classical is probably the easiest to get into (tchaikovsky is tender) but it also has difficult periods (chopin isn't a good place to start as that'll take many, many listens to understand)

Vivaldi and beethoven are good ole timers to consider as they've been rather popularized and will bring familiarity