For portals there would be a size limitation.. Probably around 2 meters or so in height and width. The portals work similarly to portals in the videogame "Portal" (portal is going to be said a lot) so essentially there is a limit of two portals. You walk through Portal A and come out B which is rather simple. There is a limit on distance you can separate both A and B which would be (just doing an estimate) 50 meters. Within this limit (this is where potential abuse comes from) however there is a possibility to place portals in such a way that an object being sent through will fall endlessly. Its impossible for a portal to close in such a way it can tear apart the object being sent through. To put it simply it can't cut a person in half nor can it trap them and even if something can't fit through it will simply pop out. 

I may have more limitations in mind, but these are just the first few I was thinking of to keep my character on the low end of the power spectrum. 

Now for teleportation the limit on distance would be similar to the portals. Its impossible to teleport specific objects unless it is being teleported along with the hero. That said it isn't possible to teleport specific areas of someone's body (mainly to avoid silly things like "lol your heart's gone!) only the entire body. There is a mass and weight limit making it impossible to teleport with a car, but maybe a trashcan or possibly a bicycle. Teleportation in general will be limited to the Hero (or villain) and anything he/she will be in physical contact with.

This is it for now I think. At the moment I do think a hero with average physical ability would be powerful against most low lvl human opponents. Anyone that is fast, stealthy and large could easily get around this.