Thin, but sturdy pieces of paper (playing cards, bits of paper box packaging) helped me a lot when trying to open my screen. The plastic picks are useful, but very slippery so you should use extra caution when applying pressure with those.
It was my first time doing a battery replacement and I seem to have somehow managed to put it together.
However, after I completed the reassembly I noticed that the phone was not charging. I had to re-open the phone and had to do some self troubleshooting and it turns out the bottom part of the interconnect cable was not fitted in.
Quick fix, but if you want to save yourself the trouble of potentially having to re-open up your phone, I would suggest that after you place your replacement battery into place - connect your display to the display connecter to see if the battery works and charges properly before closing up.