I know the saying is rather later than never and that is often true, and I do feel it is a good move on your part. The S3 is a great phone, and even with a lot of the newer phones on the market, the improvements they offer are fairly minimal and wouldn't affect the general user.
Welcome also to the era of the smartphone - when you start to learn exactly what your phone is capable of, you might just lose your partner as it entrances you with its bounty (but don't worry your phone will never leave you - unless of course you forget it.....
I carry one device with me - my S3 - its my phone, my snapshot camera, my book (in this case it carries about 567 books), my music player (about 15 albums loaded to the SD card and another 20 available via Google play music or whatever they are calling it these days), my entertainment module - always enough juice to play some really entertaining games for a couple of hours or a couple of minutes - its actually been weeks since I last used the PS3 - but there are really other reasons to that); my movie player (been catching up on TV and movies on the my journey to and from work on the days I go into the office), my newspaper (I am old school and still use a RSS reader to capture and read my news - its great as it can cache the news so I can read it offline from a variety of sources), my computer - always use it for e-mail and most of my web browsing - (use the PC for work and for general forum as I tend to type a lot and that is easier on the PC), my calculator, my sports catch up and news and score distributor, my second memory - stores all my contact details and useful info about people, and then there are all those other apps - its potential with these is absolutely amazing.
Some helpful tips -
GPS, Bluetooth and other connection systems - don't have them on unless you need them - they drain battery. That includes syncing mail etc - rather use the autosync option manually - as and when you need it. Unless you really need something syncing regularly set the sync option in the app to once a day or every couple of hours.
You can even get apps that create profiles and will change those profiles based on time, location or other switch - in those profiles you can change settings including syncing i.e. at 12am my phone switches off all connections including volume etc - so my sleep isn't disturbed - around 5am it switches them all back on, but keeps the phone silent, but also switches sync on, then before my alarm goes off it switchs profiles again so that volumes go up etc. So I wake to a fully synced phone with all my latest news, emails etc, without having to do anything - the phone has done it all for me, but hasn't beeped all night long. Make it work for you not the other way around.
Wifi - when at home keep this on, when not at home take it off. While it can be faster to use it in open areas don't forget you aren't secure, for any secure browsing use your mobile data. Set your limits in the settings area under mobile data so that don't run foul of your limit.
I use approx 250MB each month so you should be fine - I use approx 3GB of wifi data at the same time - make sure you do updates of apps etc when on wifi at home.
Make a point of going into each app and looking at the settings, change them to set up each app the way you think it should work. Don't assume it set up as per how you think it should be - in most cases the app is set up how the developer thinks it should be - and some of these people are very strange......
Most people have moved on from the S3 as it is at the end of its life span (it will not be upgraded with newer versions of kitkat) most people have had it for two years and thus the battery is wearing down and probably the phone too (they really don't make smartphones for longevity).
I am not on this forum every day but do pick up normally at least once a week, so if it is something desperate PM myself or Ratty (he is being very humble and knows as much as I do), but it is more difficult to explain something when you don't have that model available to detail the instructions.
During our time with the S3 we have pretty much catalogued every issue and a solution, so your quickest option really is to search for it first on this forum. If you can't find the solution or don't understand it then please do post a query and we will try and resolve it.