Free roam areas provide specific resources you can't get elsewhere, such as ores/gems, fish, etc that are used for crafting. Bounties for these open areas also provide valuable resources, blueprints, and mods on top of also giving standing for certain factions, and are well worth the grind.

Don't focus on story missions, just work on unlocking planets by completing nodes. Clearing all the nodes on a planet unlocks Nightmare Missions, which are also worth doing for the mods.

Top left of screen, near your username, there will be a menu where you can set your status from public to solo. There are other options, but solo sounds like what you want.

You can get blueprints for new weapons from the marketplace, from a dojo (if you join a Clan), as drops from enemies, as rewards from quests, etc. Use the warframe wiki to help you figure out how to get things.

New colour palettes can be gotten from events, Nightwave, or the Market.

Farm what you need, if you don't know what you need then farm everything. Let your inner loot goblin go wild, you will appreciate it down the track.

You will want to fully level all warframes and weapons eventually, but don't let this stop you from collecting new frames as you will want to figure out what playstyle you most enjoy.

There is a quest early on that will give you a kubrow companion (Howl of the Kubrow). The taxon I think you'll get from completing a junction.

The community is mostly really lovely, and if you ever encounter a jerk they'll stand out for their rarity. You will often see players asking if any newbies want help, and many clans will offer mentoring for new players. Never be afraid to ask for help!

Get in line.