Install WordPress or woo-commerce 1st?
WooCommerce is a WordPress plugin or addon.
As such, you can only install WooCommerce on an active WordPress site: you cannot install WooCommerce without WordPress… much the same way as you cannot install a smartphone app without a smartphone.
And note the correct brand names (including the capitalized letters): WordPress and WooCommerce, not “word-press” and “woo-commerce”.
1) I read both (word-press and woo-commerce) were free to install and use, is that true?
WordPress is 100% free generic site builder. But there are thousands of independently-developed add-ons (called plugins) that add additional capabilities to WordPress.
Some of these plugins are 100% free, some are paid-only, and some (perhaps most) have a free “lite” version with paid upgrades.
WooCommerce is one of these independently developed plugins: it adds e-commerce capabilities to WordPress. It’s 100% free, but there are also lots of free and paid add-ons that add additional functionality to the standard free WooCommerce.
2) When I was going to install word-press I HAD to pick a website template (didn’t finish install), is that something I have to do to start word-press installation?
A theme (perhaps this is what you’re calling “template”) is what gives the design of a WordPress site. A new WordPress installation always comes with a default theme so the newly-installed WordPress site can work out of the box. But what you’re describing sounds like your hosting provider has some WordPress auto-installer that’s presenting some preset options to you.
Note that you can always switch from one theme to another, though the new theme will likely need some configurations and tweaks to give you the desired look and feel.
3) I’ve read woo-commerce is the way to go, DO I INSTALL IT 1ST?
See above.
4) Do I download either and un-zip or is there another way.
From your post above, it sounds like your host has a WordPress auto-installer available and I’ll advise you to use that.
But if you prefer to install WordPress manually, here’s the official manual installation guide: https://developer.www.ads-software.com/advanced-administration/before-install/howto-install/
Once WordPress is installed, you can easily find and install the WooCommerce plugin (and thousands of other plugins and themes) directly from the WordPress dashboard.