This is unfortunately very subjective, varying both on the data you have size-wise, its importance, and so forth. You may even want different regimes for different chunks of your data: syncing your collection of large photo files with your offsite backups weekly (or on-demand as you add a new set from an outing), but synching documents and financial stuff daily.
As for how many versions you have to remeber that a backup deals with two very different sets of fault scenarious: hardware error and human error. For the hardware dying situation you only need the one good backup, so at least two (in case the failure happens while updating the current one), preferably the traditional three. For covering human error it isn't a case of how many copies to keep, but how far back those copies should go. If you were to accidentally delete a file for instance how long would it be before you noticed? You need a backup going that far back plus a little. A not uncommon choice is three daily copies and three monthly ones, but there are no hard and fast rules (or even genberally good rules of thumb) here - only you know how important your data is and so how much effort you need to take to protect it.
Personally I use snapshots-via-rsync using a technique similar to those covered in http://www.mikerubel.org/computers/rsync_snapshots/ (the article is old, but still relevant) - there are other ways to acheive a similar effect too which might be easier if you are a beginner (http://rdiff-backup.nongnu.org/ seems popular, but I've not used it myself so can't comment more specifically). I have monthly snapshots going back over a year and daily ones for over a month, and as most of it doesn't change much it doesn't take all that much space than a complete copy or two. An important thing to consider with any solution like this though is that corruption in your backup set can affect all snapshots at once, so I recommend at least two disconnected copies of the data so you have at least two physical copies of each file meaning corruption in one of your collections of snapshots doesn't affect all the "copies" you have.