I replaced my '03 Sentra with an '06 Civic LX in August. I did an oil & filter change after the first 1,500 miles, and then again after the next 1,500 miles. Overkill? Maybe, but I like to do frequent changes on brand new engines.
I used Pennzoil 5W-20 the first time and Mobil 1 5W-20 (with 1 quart of 0W-20 thrown in) right before winter was supposed to set in in December.
I'd never drain the oil and leave the old filter (with a half pint of the dirtiest oil in it) on the engine.
I plan on using 3,000-5,000 mile intervals regardless of what R2D2 says. I make lots of short trips (my commute is 7 miles - 12 minutes.). That'll be about 3 oil changes per year. I stocked up on $1.55 Havoline 5W-20 and 2-for-1 Pennzoil Platinum (GrpIII - $2.84 per quart) and have enough for the next year and then some.
Filters? I'm pretty sure the filters I had for my Sentra (OEM Nissan) will fit the Civic. I have also used Purolator (regular and pure-One). Getting these on sale (Advance Auto Parts) is a great deal.