First time in Prague...

You can take a bus to a Metro line and then ride into the center city. We came in by train and took an early morning private taxi ride to the airport. It's maybe 8 miles out of town.

See Booking.com and AirBnB.com for accommodations. There are a bunch of rooms in the city.

We took the "Free Walking Tour" first day, and their Pub Crawl Tour the first night. We found the nightlife to be great and beer cheap. Otherwise, it's not the inexpensive city it was 10 years ago.

Arcadia Residence is well located and a perfect place for first-timers to stay as the staff is so helpful and welcoming. They will arrange for an airport pick up for you.

I took the bus to the Metro when I flew into Prague last March. I read how to do it on wiki travel, and found it very easy and inexpensive. (for what it's worth, I'm a solo female traveler who does not speak Czech beyond a dozen travel words, and had no difficulties.)

Do you have Rick Steves Prague And The Czech Republic? In addition to listing a bunch of accommodation options, he also details the various ways to get in from the airport, with costs and exact steps needed. He also has details about getting around (while you can walk much of the time, trams are very handy; the Metro is less useful, but works fine for some places).

I am a regular visitor to Prague and there are many options to get from the airport to the city centre and depends on where you are staying. Things changes on some routes recently.
https://community.ricksteves.com/travel-forum/czech/changes-to-metro-system-in-prague
loads of accommodation options too. look at Booking.com for some good ideas and at this link for cheap options.
http://www.livingprague.com/hostel.
once you find somewhere to stay let me know and I can work out the transport options for you.
The transport system in the city is excellent and cheap.

Thanks for all the helpful suggestions. Rick's Forums are great!

you are welcome Barb, as I said let me know where you are staying and I will help with transport links. I am back in Prague during the last week of October .When are you visiting.

We stayed at the U Zlateho Jelena which was very affordable, with a decent breakfast, and is only like a 3 minute walk from the Stare Mesto (but far enough away that you weren't right on top of it). It was about as convenient of a location as you could get. I would recommend asking for an interior room, however, as the ones above the street got a little loud when the bars got out.

Our hotel offered a private car that picked us up at the airport and dropped us off right at our hotel, and I believe it was only about $20 USD, or something like that. I'm sure there are cheaper ways, but that was so convenient and reasonable that we decided to do it.