The best way would be to run through the Ubuntu Friendly Test Suite. Simply search for "Friendly" in the Apps lens, and run the "System Testing" app. This already has all hardware related cases, and is a quick, easy way to test through all hardware enablement test cases. More info can be found here: https://friendly.ubuntu.com/participate/
Yes, absolutely you can make it work with a full install. To make the change permanent in your installed Ubuntu you will need to edit the grub configuration file and add the nomodeset option so that it loads each time Ubuntu boots. It's more complicated to set it to install this way automatically, and it's probably not normally desirable to do so. If you want an easy way to do this I suggest you edit the config file as per the following instructions and simply copy this file to the correct location during installation.
To add nomodeset to the grub config do the following
1) Press CtrlAltF1 to open the console
2) Log in to the console using the username and password you entered during the install
3) Start editing the /etc/default/grub file with
sudo nano /etc/default/grub
4) Find the line that reads:
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash"
and change it to read:
GRUB_CMDLINE_LINUX_DEFAULT="quiet splash nomodeset"
5) To save the file press Ctrlo then exit the editor with Ctrlx
6) You'll need to update grub with the new default config
sudo update-grub
7) Reboot and marvel at your wonderful new Ubuntu system!
sudo reboot
Optional:
If you want to change the grub configuration during the install before it completes, the file you will need to change will be /target/etc/default/grub because that is where the root filesystem is mounted during installation. As long as you do this before grub is configured then it will be affective from the first boot of the new installation.
References
Ubuntu Forums
Ubuntu Wiki
Best Answer
This is a very similar question as this AU Question and step-by-step answer.
Ignore the "nightly download" part of the answer - just use the ISO you have downloaded to install onto a USB stick.
Once installed, you can Activate the broadcom drivers in the Additional Hardware window.