As for what you should provide or how you should make these structures; that's up to you. You'll want them to be wide enough to hold your large, fully grown iguana. Instead of using branches, though, purchase planks of wood and then cover them completely with the same materials you've covered your flooring with. Some of the best material to do this with is indoor/outdoor carpeting.
You'll want to cover the entire board and the climbing structures with this carpeting. This will give them their necessary grip to grab onto their structure to move around.
You'll want to completely wrap the board with the carpeting and then secure it. Don't leave anything to be exposed as this can cause tears and injury to your iguana. Again, just like the flooring, cover the wood with vinyl sheets that can be wiped down. Then, wrap in the carpeting. You'll have to remove the carpeting and clean regularly so make sure it's easy to do this.
Within your habitat, you'll need to put in your food and water bowls. They must be sturdy otherwise your pet will knock them over. In addition, don't allow them to be too tall for your guy to reach in and take a drink.
In addition to providing a bowl for food and water, you'll want to include a container that your iguana can get into and out of easily so that he or she can have a nice soak. Fill it just slightly with water as a small amount of water can cause your iguana to drown. In addition, make sure that as he is climbing in and out, the container is not going to tip on him.
You'll have to monitor his use of this soaking tub for a while, especially when he is younger as they often struggle with water and can drown. In addition, they love to use it for a bathroom! So, make sure you monitor and clean this tub often. Don't skip it though as they need it to help them to shed their skin.
Another area to provide for your iguana within their habitat is that of a hiding place. They really like to get away and hide from view for a bit during each day. You can purchase or build your own hiding structures, which is especially important for younger iguanas.
As they get older, though, your iguana won't need an entire box to hide in. Instead, he's more interested in having a location that may be just a bit out of the way, such as an area that may have an obstructed view by design of the climbing structures.