I have an iPhone 4S with multiple backups in my computer and I'd like to buy a new iPhone.
Can I connect the new device to the computer and immediately store all the content from the previous iPhone? I want to move all the photos, messages, etc.
The easiest way to do this is to do a full backup of your iPhone 4s via iTunes.
Then you would connect the new iPhone to iTunes as well and then do a Restore from the iPhone 4s backup to your new iPhone.
The iPhone 4s was available in various sizes, namely 8GB, 16GB, 32GB and 64GB. So you will need to ensure that your new iPhone has as a minimum the same capacity as your old one.
You should also select the "Encrypt local backup" option as this will "allow account passwords, Health and HomeKit data to be backed up". Of course, in your specific case, an iPhone 4S doesn't have health and home data.
I would do it through iTunes using the USB cable. iClould is all well and good if you have more storage on there than the paltry 5Gb Apple gives you as standard. I was never able to backup fully everything from my phone to iCloud as it was over 15Gb including all the photos and videos. Doing it using iTunes is simple and just takes a little time is all.
Just a little FYI... There are some apps that won't be restored from a full backup. I owned the app 'Music D/L' which let you download MP3 files from a website and listen to them on the phone. Since it has been removed from the app store, you don't get it back on a restore. I'm not sure if this applies to every app that gets removed or deleted from the app store.
I would recommend using iCloud as your backup solution.
iCloud backups will restore a new iPhone just like iTunes and do not require the new iPhone to have equal or greater storage capacity. Also you can setup iCloud to backup whenever your iPhone is connected to wifi and power and locked.
Most of your important is stored in iCloud meaning if your machine is no longer or your iTunes backups are gone, your information is stored securely and you can restore your iPhone just by logging into your iTunes account from any new iPhone.
Go to Settings > iCloud > Backups and turn it on to get started.
Yes, I would do the restore through the iCloud backup feature over a wifi network. The process is very step by step and simple. Do keep in mind that certain things such as purchased ringtones will not transfer from an old phone to a new one.
Check out this link: https://support.apple.com/kb/ph12521?locale=en_US