Question about collections

Hello,
I am creating simple (for now :D) game (for learning purpose) and would like to ask you for advise.
I would like to ask you which collection type should i use.
I have LinkedList named Isradimai (Inventions) which contains all Isradimas (Invention) type objects. (For now it only contains 20 but later it could contain 100-400 objects). Also there is another LinkedList named Ismintis (Wisdom) which contains only discovered inventions (Isradimas objects). And there also is 2 more LinkedLists named galimiIsradimai (available inventions) and galimiDarbai(available jobs). GalimiIsradimai contains only new discoverable Isradimas object and are show to player to pick new invention. GalimiIsradimai are populated by cloning Isradimai and then removing all that are contained in Ismintis. Then i iterate over it and examine each object to see if it fits needed requirements. If it fails it is removed. Each time player “invents” new invention i clear and repopulate galimiIsradimai and player have a new list of possible inventions it also clears and repopulates galimiDarbai.
GalimiDarbai contains all available actions for player. Sometimes inventing new inventions unlocks new actions for player to perform.That list is populated by iterating over Ismintis “and” Darbai (HashMap). If Isradimas object (contained in Ismintis) unlocks new action i look in HashMap and put received Darbas object in galimiDarbai.
Everything works very well. But one day i got idea that it could be better to replace all LinkedList to HashMap. So what do you think?
If you see some flaws in my design please post them too

Thanks in advance.
P.S. Sorry if i made some mistakes

I don’t see any flaws. The main advantage of a HashMap to a LinkedList, is that you can retrieve the object faster when you have the key. I would make the Isradimai a HashMap for faster retrieval.
For the Discoverable list, I would create a HashMap, the key being the discovering event (a level or whatever), and the value to be a list of Isradimai keys.

Your choice should really be down to HashMap or ArrayList. Other Map implementations are for specialty purposes, and there is hardly any circumstance whatsoever where LinkedList is a better option than ArrayList; LinkedList even fails for functional data structures, since it isn’t recursively defined.

Edit: naturally, the choice between HashMap and ArrayList wouldn’t be down to which performs better, but which operations you actually need.

Thanks for your answers.