Its best if you figure out the tips before you leave, follow the cruiselines tipping guidelines and you can adjust it if you need to. Just have that cash ready for the last night when they give you the envelopes, then simply put the approporate cash in each envelope. While you are on board, you will be using your "sign&sail" card to pay for any purchases, drinks, etc. They will add a 15% tip on to each drink order, so you don't need to tip any extra. All these charges will go on to the credit card you give them when you embark.
As for sunning on the pool deck, yes there are plenty of chairs, although many right by the pool will be the first to be used, you may have to go a little distance from the pool, but you should be able to find a chair. Only time when it does get difficult, would be on a "sea" day, everyone wants to get out on the pool deck.
Since this is your first cruise, it may be a good idea to book through the cruiseship, although there are plenty you can pre-book before you go without using the cruiseline's excursions.
We cruised on Radiance earlier this year in the Southern CAribbean and this ship right now is my all time favorite, its beautiful, you'll love it.
YOu also may want to read through the section here for "first cruisers", lots of tips and info:
Have a great time!