While my site is mainly about the Euro Coins per se, some general comments on coin care are most probably not inappropriate.
To what extent you follow the ideas set out below will depend to a large extent on how you view your hobby - do you wish to simply collect the Euro coins that fall into your hands and order them into the appropriate slot or do you wish to slowly build up a valuable collection - or perhaps both?
I, in fact, do both.
For my " used coins collection" I get what I can from family and friends who have to search through wallets and purses to find "my missing coins".
My "mint coin collection" I am building up by purchases from reputable dealers and by adding what I want to birthday and Christmas wish lists which are presented to my wife and sons!
Mint-Fresh uncirculated coins.
Always wash your hands before handling your coins as the sweat on your hands contains acids and oils that can impair the mint quality of the coins. Better still would be to wear a pair of cotton gloves while handling your coins. In fact acceptable ctton gloves are so cheap it really makes no sense to not getting any if you are serious about building up a respectable coin collection.
Make a point of always holding your coins between thumb and index finger, thereby avoiding contact with the surface of the coin.
When you lay your coins down, do it on a flat soft surface such as a clean cotton cloth or felt and avoid moving them while they are on the surface. Clearly if moved across a surface - particularly a hard surface, damage is pre-ordained.
While cleaning coins is frowned upon by many a numismatist (fancy name for coin-collector!), in the case of Euro coins that have been in circulation, I see no harm in this. Here we are not dealing with valuable rare coins where removing the patina of history is likely to reduce their value.
Virtually all Euro coins in circulation are worth their face value - no more and no less and this will not change whether they are cleaned or not!
A coin from which the grime of circulation has been removed and which approaches to an extent the lustre it had when first minted is certainly more attractive.
This is particularly true of the 1, 2 and 5 cent Euro coins which slowly attain an unattractive brown colour after several months in circulation.
There are several cleaning pastes on sale which do an excellent job. If you are reluctant to spend money there however, you will find that ordinary toothpaste also does a reasonably good job.
I also use an ultra sound bath - these are not unreasonably priced and can be used to clean other things such as spectacles!! I must add though, that I have found that while an ultra sound bath brings back a little extra lustre - it is not much.
The more expensive Euro coins you will almost certainly have to buy and these presumably will be mint fresh and therefore need no cleaning.