The following procedure describes the basic needs for moving your magento-shop to another server. There might be additional things to consider (changing domains, DNS, PHP-Configuration, tools & programms on your server) which need to take care of on your own.
1. Backup files in your Magento directory on your old server:
You might empty your var/cache, var/session, var/report and var/log directory first to save space and speed up the backup
2. Create a database dump on your old server:
Use phpMyAdmin, Chive or via console with mysqldump, n98-magerun
3. Set up directory structure for files and create database + user on your new server
4. Move files and database dump to your new server: via FTP, SSH,...
5. Extract file-backup to your new magento directory
6. Check and set file-permissions
Usually 644 for files and 755 for folders.
See also this question for more information: What permissions should I give /var and /media?
7. Import database-dump on your new server:
Use phpMyAdmin, Chive or via console with mysql, n98-magerun
8. Update new database-settings in app/etc/local.xml
9. Update URLs in core_config_data:
You can edit the base_url via Web-Frontend (phpMyAdmin, Chive,...) or use these SQL-statements. You might need to edit the urls for your stores also.
Look for path ="web/unsecure/base_url" and path="web/secure/base_url" in the core_config_data table.
10. Empty var/cache, var/session, var/report, var/log (if you did not do that before you created the backup on the old server)
11. Reindex your data: catalog url rewrites
12. Enjoy your beer!
First off, welcome to the wide world of Magento! Here's a great article with details on different ways to backup Magento that give a good breakdown for a lot of this. The article is geared towards a running server setup but mostly the same rules apply for your local MAMP setup. A lot of pertinent information can be found there.
If I disable the Apache and MySQL servers would it then be enough to copy the entirety of > the MAMP folder and Magento folder to offsite storage periodically?
No need to disable Apache / MySQL. You can backup Magento with everything running. Essentially Magento will either 1) make changes to files or 2) make changes to the database. Most backup methods for the files (drag / drop files to backup, use shell commands like cp or rsync, etc.) will work fine if files are actively being modified such as the var/cache within Magento. The only thing that will happen is maybe at the time of copying the version you have is slightly older because it was updated right after you copied it.
Do I need to create exports of the database using PHPMyAdmin in addition to step 1?
As for MySQL, you should use the mysqldump command (more details in the blog article link above). This will have MySQL do the backup for you so no need to worry about actively using the database. The only concern is that it can add load to the host computer during backup that could slow things down but it shouldn't crash anything. You could also use PHPMyAdmin to do your backup without it crashing / harming anything (again might just slow it down).
Should I also create and then download System and Database/Media backups from inside the >Magento back-end?
Depends. If you're comfortable using command line to move, copy, rsync etc. files then I would skip the Magento backup manager. It can sometimes have issues and be a bit slower. You could use it but not needed in addition to regular backup methods.
Before backing up the entire Magento store, do I need to disable things such as indexing, >the cache, or put the store in maintenance-mode first? What impact (if any) is there when >backing up a database that is possibly in use?
No no and no. You're fine to backup an active running site. The only thing you could do to maybe save yourself a step later would be to either entirely flush the Magento cache storage before backup or just exclude the var/cache/ directory from your backups. It's automatically regenerated upon using Magento either from the Admin or front end.
As for the DB performance, again it can impact performance but that depends entirely on the size of the database and your hardware. If the site is just in dev it's likely a small database (unless you have tens of thousands of products).
Lastly, I installed the Magento folder inside of the MAMP applications folder (at the >direction of a well reviewed Magento development book). Are there any other files or >folders outside of MAMP that I should be backing up? (The database is located in: ?>Applications\MAMP\db\mysql).
I haven't used MAMP much but as for Magento it really consists of 1) the files and 2) the database. Unless it's like some of those goofy installation tools chances are all the Magento files are contained within 1 directory. If that's the case, just making a backup of that directory and then a backup of the database would be enough. Apache configs, tuned mysql settings, etc. are all a different story but with the files and database you could then re-install or setup that Magento site elsewhere (either on your MAMP or deploy to a server, etc.)
And as already stated, GIT is always nice ;)
Best Answer
The absolute simplest method.
If you have SSH access and the disk space, the easiest way is to create a tarball (archive similar to windows Zip) of your webserver doc root and a compressed mysqldump of the database to a backup folder in your home directory (above your web server doc root so it's not web accessible).
Use SFTP to download the tarball and database backup to local storage. With only two files, it goes a lot quicker and is less likely to suffer errors than a long excruciating SFTP download of each individual file in the Magento installation.
Also, if you have Amazon Web Services, you can create an S3 bucket and use S3command to copy your backup files to that (goes the quickest)
(If you have a version of Magento that has System and Database backup, DO NOT USE THESE! They often knock your site offline with a 500 error do to messing with file permissions)