If they are paid apps, they will automatically let you download them for free once you sign into the market. As far as free apps, you can obviously download them again for free. I believe you are talking about AppBrain. It makes a list of all your apps on the old phone, then when you get the new one, download that again, and your list will show up, allowing you to download them one by one. Keep in mind, this does NOT backup the app's data, like Angry birds saved games. To backup the app's data, you need to be rooted.
For texts, you can use SMS Backup and Restore. Backup the texts on the old phone, put the SD card in the new one, download the app again, and restore them.