You can import this any moment in any Bitcoin wallet client, make sure it is verified safe. You can find a whole list here: https://bitcoin.org/en/choose-your-wallet. So uninstalling won't be a problem as long as you have your private key stored. The fork can not accidentally change your BTC to BTG, the fork is a copy of Bitcoin's current blockchain which will split after 25 October. Every BTC you have now will correspond to one BTG. Both wallets will have the same private key, so make sure you import it to a verified BTG client. Otherwise your key can get stolen. A good solution for this is sending your BTC to a new wallet after 25 October and then importing the old wallet key in a BTG client. The safest wallet is just personal preference, Armory is in my opinion the safest wallet. But it is quite complicated. Electrum or Core are more user friendly.
To make sure you don't lose your forked coins, wait at least 12 hours after the work.
After that it's totally safe.
Sounds ok, but I read that wallets automatically follow the “longest” blockchain, does this mean that my wallet can decide on its own that my coins are BTG not BTC? How to be sure then after the fork if I buy BTC on local bitcoins and send the purchased BTC to my wallet it will come in my wallet as BTC not BTG?
Any further clarification is highly appreciated.