Range extenders come in all sorts of guises..
The best ones, will do WDS which allows a system to fully integrate the extender..
Apple routers use a variant of WDS to extend by another Apple router.. but it is a closed system. You cannot use WDS between brands generally and certainly NOT with apple routers.
Then you have your standard universal repeater. These are much poorer as they pick up a signal and use it effectively to connect to another router. There are huge numbers of rules .. for example not all repeaters work with WPA2 security. In fact most older ones do not.
Step 1 is to make sure your wireless name on the Apple router is short, no spaces and pure alphanumerics..
eg TCwifi
The password must also be pure alphanumeric mixed case and numbers.. no special characters.
Step 2. I recommend you start with no password at all.. ie no security and see if you can get the setup to work.
Remember Netgear extenders will be designed to extend netgear routers and you might need to set the IP manually .. by default the TC will have 10.0.1.1 IP with range of 2-200 for dhcp. The netgear will definitely use 192.168.x.x with the extender needing IP set in the range of the TC. Read the manual for that.
Step 3. Once you get it working without wireless security.. you are then ready to see how well it copes with WPA.. try WPA2 Personal with rules as in step 1.. if that fails try the lower security WPA1/WPA2.
If both fail your Netgear products will not work without WEP which is no longer viable security for wireless unless you live 2km from human habitation.. in which case you may as well go back to step 2.. and use none.
Alternatives.
1. Buy more airports.. they are simple to setup to extend wireless.
You don't need expensive AC model extreme or TC.. you can buy Express or older model Extreme.. the Gen5 work very well if you can pick them up second hand.
2. Run ethernet to other areas of the house and plug the extenders in if they do WAP mode (most do).
Expensive but this is the best.. an alternative is to use powerline extenders. They do work for many people very well.. but power cabling in the house is not certain.. one person gets 50Mbps through the same adapters as another person gets 5Mbps.
3. Use your existing DSL modem router in wireless router or WAP mode plugged into the TC. I am guessing this is a netgear brand .. hence the netgear extenders. It can be used in WAN bypass mode if it is older model without WAN port or WAP mode. Google it but if you need help I can give you the details. The extenders can then work as before and it will work alongside the TC wireless. Since this is only 2.4ghz you might need to do some channel configuration but that is not hard.