Infected troops are best used for attacking another player’s city. The reason for this is that they are strong against defenses, whereas defenses are strong against your living troops (different defenses are strong against different troops), and every one of your living troops is weak against other players’ defenses.
However, living troops are best used to attack infected cities and as defenders of your own city, since living troops are strong against all infected troops. Living troops are far less likely to die in defense of your city (everyone dies against infected cities, usually) and when they get killed, they will just get sent to the hospital (depending on if the hospital has room for them or not).
One of the best reasons to attack the infected cities is to try to capture enemy zombie leaders. You can have up to four different types of zombie leaders at a time, and they are unlocked only by capturing them from an infected city or from a rival player, as opposed to regular zombies which can be trained at any time just like troops.
Eventually you might want to start your own alliance. The biggest challenge at this point is to find people to add to your army. You’ll have to hit the ground running to grow your alliance initially. Find new players and send them invites, and find people in global chat who are asking about alliances to join, and convince them to join your alliance by talking to them one on one rather than by simply spamming global to find alliance members.
Save your teleports for when you really need them. The best example is when you are in an alliance, and the leader finds a good spot to move to. Move there with the rest of the alliance and if you successfully crowd an area, it will be highly unlikely that you will be attacked, unless you end up in a full scale war with another alliance.
Or, if you are trying to start your own alliance, teleport to an area in the middle of a bunch of newbies. Recruit them to your alliance if they are active. This gives you the option of playing a little bit dirty if you want to – using mafia style protection-racket tactics on them.