I would suggest the following:
1, Spend some time sorting the cents in the medicine bottles; separate/group them by date and mint mark.
2. If you find that you have multiples of each date/mint mark combo, I would go with either 2x2 cardboard-mylar holders or non-PVC pocket flips. Buy an appropriate number of non-PVC 2x2 pages to hold all of your coins, place the coins in them and make your own album with a binder.
3. If you only have one of each cent (or nearly so) it might make more sense to pick up a dedicated album to store them, and continue to keep the lower-grade extras in the bottles.
Hope that helps!
There shouldn't be any harm in removing the coins from the Littleton bags and placing them in 2x2s or flips. Most collectors I've encountered remove them.
Here's a link to a brief, but useful introduction/overview of coin storage options (it is aimed at beginners):
https://www.thesprucecrafts.com/typ...ders-768327/