I always buy a spare battery since I'm often not near an outlet but also in case of emergency or for troubleshooting purposes if the original battery malfunctions, but of course only you can answer if it's worth the cost to you.
I always recommend ONLY buying original manufacturer batteries and only buying from authorized resellers or the manufacturer. I know a lot of people like to go the cheaper route and I used to be one of them before I bought what ended up to be fake (sold as OEM and looked like OEM in every little detail) Samsung batteries off ebay for a previous phone and learned my lesson when they fried the insides of my phone. I first found out they were fake because the NFC wasn't working despite have Near Field Communication written on them like my original. The seller insisted it was an OEM battery and must just be defective and agreed to replace it. I had ordered two and ended up replacing them twice and of course none of the batteries actually had NFC despite the markings because they were fake. Since I had all these batteries now I figured I would just use them as backups when I didn't need NFC. One of them heated up my phone so high that when I picked it up because I saw that it had suddenly shut down, it burned my hand and after it cooled down enough to touch it, when I opened the back it was melted inside. Of course I had no recourse since they were fake.
So that's my warning about buying non-OEM replacement batteries or buying what is sold as and looks like OEM batteries from ebay, amazon, or anyplace that is not an authorized reseller. As far as how many spare batteries to buy, buy what you expect you will need in the next 6 months or so. Battery life declines with age even when the battery is not being used. You can expect a year or so of decent battery life. If you bought several spares now planning for the future - say you expect to use the phone for the next 2 years - all your batteries capacities will have declined a year from now. If you buy one now (or two if you have reason to think you will need more in the immediate future) then 6 or 9 or 12 months from now you can buy a fresh one that will have 100% capacity at that time instead of the lessened capacity of the one that's been sitting in your drawer for a year.
There is a battery charger on the samsung website, under accessories for the Note 3, that comes with a spare battery and I am getting that one myself.