Here is an example of a TP/SMF site: Planet Descent
Now I will run down what I did. First, Tiny Portal provides the front page, the horizontal menu and above are mostly stock SMF, the only thing I did was a little re-arranging of the horizontal menu. (the one with Home, Forum, etc...)
Picture of the Day is just an item in a certain board that is pulled automatically whenever someone puts a new post. Same with Soupe Du Jour and the New section. All the code to do this is provided with TP, just configure it how you want it. Below the picture of the day is a block with custom php and java-script, displaying items from the Zazzle store. Script provided by Zazzle, with some minor tweaks, copy-pasted into a block. Below the Soupe, is the poll. This was custom code written by JPDeni, following my request in the forum here. It is now available in the block code section here.
In the forum there are blocks in the right coulumn showing recent posts, and if you were a member you would also see a shoutbox. These are also provided with TP, and just require some setup choices to be made.
The Media section is provided by Aeva Media and has no connection to TP, but TP blocks are able to show in the Media section. Right now I only have the shoutbox on but adding recent posts or whatever is just a matter of selecting options.
The Files section is provided by TP. I hard coded the link in the menu myself, but other than that it is just the TP downloads module as provided.
I have also added Articles to the menu, but sorry that section isn't open to the public yet.
Now about themes. Any theme that works with the current version of SMF should work with the current version of TP. If your using SMF 1.x, you'll need a 1.x theme, and if 2.x you need a 2.x theme. Every
theme that I had tried worked reasonably
well with TP, however most of them required some minor tweaks. The theme on my site now is a custom theme I made from a copy of the default theme. I made 2 version, the light on dark as default, and a dark on light as some members complained about the readability of the dark theme.
I strongly suggest that you set up a test site and experiment for a while if you already have an active site. Most hosts will allow you to set up a sub-domain, like 'test.mysite.net'. I did this before rolling out custom themes and to run through upgrading. It really helped to get member input about changes I was contemplating. And to familiarize myself with the process, in order to minimize downtime.