Stay far, far away from tuning boxes. They are NOT a good idea. They work by falsifying signals from sensors on the engine to the ECU, tricking the ECU in to providing more fuel. The problem is the ECU no longer knows what is going on, so it is not properly in control of the engine. Even worse, quite a lot of the ECU parameters are 'adaptive' meaning that the ECU will figure out over time that it is being lied to and adjust itself accordingly. This feature is in place to deal with the variations between sensors and vehicles. The result is that the initial effects of the tuning box will fade away over time.
Rather than tricking inputs to the ECU to make it do the 'wrong' thing, you want a new program loaded in to the ECU to make it do what you want. Where things get tricky is that the 1Z/AHU need to be 'chipped' rather than just have a file uploaded to them. If you poke around on tdiclub.com you might be able to find someone who is selling an ECU that has already been chipped, or a set of chips. I think some of the tuners (probably Malone) are still doing tunes for the older ECUs too. It is MUCH better to tell the ECU that you want it to give you more HP and have it do its job than to try and trick it in to giving more power without it knowing what is going on.
Going larger on the injectors is a very good thing to do. The engine will respond nicely to larger injectors even without any other tuning changes. How big you go depends on your longer term goals and whether or not you intend to get a tune - you can increase the injector size a little with the stock tune, but if you want anything significantly larger you need the tune to go with it - that's back to the ECU knowing about what is going on. Injectors and tuning changes ideally should be done at the same time.