What is the best way to grind for ip

Probably ARAMs. Those matches don't usually take long and you get to try out champs you don't typically play. Good luck!

Arams and normals are the easiest way without being stressful. Especially while having a first win of the day bonus. AI doesn't give enough to make it worth it, but they are the fastest and you technically can win in like 10-15 minutes if you're good enough.

Also! You could kind of bypass the high price of some champions by buy the Champion Token for hextech crafting :P It's 1700ip and gives you a champion shard. Just buy 3 and you're guaranteed a champion (once you reroll the 3 shards together). Granted it's random, but if you only have 4800-6300 champions left I recommend doing it. I only have two champions left to go, so I've been doing that often since 1700 is easy to reach with First win and quick games~

Also, the cost of runes goes way up on the last tier for little benefit, so it's possible to save some gold from those purchases