If you honestly have no pressing reason to play online or access the PlayStation Store and browse the new content then I suggest you avoid it for a little while.
Error messages have been popping up at regular intervals while surfing through content in the UK, US and South African stores. Even signing into the PSN is being met with errors on occasion but if you keep trying you will get in eventually.
Once downloads begin however they are luckily continuing without an issue, it’s just getting them to start downloading that’s the problem at the moment.
This is probably due to the sheer amount of people accessing the service after the news that the store had returned broke and the in-store errors are just due to the service still being ironed out, everything should be back to normal by tomorrow.