My take on screen protectors is that you have 2 types of protection. With a regular peta film one (talking about quality 3H hardness from reputable companies) you get a basic scratch resistance type of protection. It will be thinner but at the expense of a more plasticy feel, some trade off in touch sensitivity, and in some cases a subtle rainbow effect under fluorescent lights. And if you drop your phone and it hits a screen on uneven surface - your screen will crack. With a 2nd type of protection, you use a tempered glass which supposed to give you the best sensitivity and clarify, easier to wipe off fingerprints (trust me, even oleophobic screen protectors collect fingerprints since the coating will wear off after awhile), and a superior impact protection where glass will shatter leaving display safe. But a trade off is a thicker glass layer and no guaranteed scratch resistance, plus a much more expensive. In theory tempered glass will have at least 9H hardness rating, but after awhile even that get scratched when you have your phone in the pocket with other junk. Plus, a lot of cases are made with a thinner lip just enough to keep the display off the surface when you place the phone down, and having a thicker tempered glass makes it stick out.
If you are putting your phone into something like OBEX case - you don't really need extra screen protection. But, for example, Seidio passed on Obex for N2 (but have it for S3/S4) and most likely will skip N3 as well because they don't know how to handle S-pen port opening. If you are looking for Defender, we all know how well their plastic protector worked with N2 lol!!! For any other open face cases, I would strongly recommend either film or glass screen protector. For ultimate, go with tempered glass but do research about which case you want to use it with. As I mentioned before, N3 has a small bezel, might be a challenge for a design. As a minimum, look into a film screen protector where Spigen is always a top choice.
You can always replace a battery cover, but scratches on display will stay there staring in your face especially when N4 is released and you want to list your N3 "in mint condition"
But if you want to play russian roulette with a display, go bareback