You will need an amplifier of some sort. Again, you will develop unique preferences for different sounding amps so don't spend big yet.
Watts basically describe how powerful the amp is. More watts means more power which means more volume. If you are just going to be practicing by yourself at home, you don't need but 20 to 50 watts. If you plan on playing with a guitarist or keyboard player, you may need 200 watts. And if you plan to play in a band with a drummer right away, you need 300-400 watts. You don't want to turn up an amp more than 3/4 of the way. It sounds better to have more watts not turned up so much than fewer watts turned all the way up.
Don't be fooled thinking a big speaker means more bass. A good 10-inch speaker can deliver more bass than a cheap 18-inch speaker. Smaller speakers have a punchier sound and bigger speakers have more boominess. A 12-inch or 15-inch speaker should serve you well.
Don't wait to buy an amp. You need something to hear yourself or you will ruin your technique! Go buy something to get going.
Practice hard and save money. When you learn how to play something, go around to all the music stores in town and play every bass and amp you can find. After a while you will begin to notice the subtle differences between various basses and amps. Then you can make your own decision based on your newly developed ears, eyes and hands.