.. the chain that will be chosen as the dominatn one is that with the most nodes running up. So if you support Bitcoin Core you must run a Bitcoin Core node and accept and check transactions with it.
good luck
Yes. Take an old computer and run a node. Thousands of people should do that. Tens of thousands. Think it over.
Now one little tip on opening the 8333 incoming connections Bitcoin Core port - in case you enabled incoming connections and UPnP in Bitcoin Core configuration, but your following checking of your 8333 port on https://bitnodes.21.co/ is showing that your 8333 port is still closed.
For those of you who (like me) don't have a static ipv4 address and get dynamic internet addresses on every router boots, I'd suggest the following :
1. Open your internet router's configuration web interface and look for your router's current external ip address (as it changes on every router boot with dynamic addresses). Remember it.
2. Then go to https://www.whatismyip.com (or any other online similar service) and remember your real external internet address.
3. Compare the two addresses. If they are equal then go to step 5. Otherwise go to the next step 4.
4. Contact your internet service provider and ask them NOT to use NAT for your router if ever possible. (that's exactly what I did and what then really allowed me to open 8333 port for incoming connections).
5. Again open your router's configuration web interface and either enable 8333 port forwarding or (what has worked for me) enable the UPnP for your IPv4 WAN connections (this setting will allow Bitcoin Core itself to open the 8333 port.
Now don't hurry up, give the Bitcoin Core application some time (from 30 minutes to a couple of hours) to establish incoming connections.