I am guessing you are not on Rocktropia since you can get both of those items free in beginner missions there, so you are probably on Calypso or Arkadia.
I will guess Calypso since it is the most common one.
Have you done all the starter missions at icarus and port atlantas?
Once that is done, I would alternate my time between starting your puny iron missions (kill 100, 500, 1000, 5000, 10,000) and using your helicopter to get to all of the teleporters on the planet you are on. (google a current map of your planet to know where they are) You can only use teleporters once you have already been to them, so you need to physicaly travel to (all but a couple of free ones they give you to start) all of them on your own, this is one of the first activities alot of players do.
Study what is the most economical weapon for your skill level in the discipline of weapons you want to use(blp or laser, rifles or pistols, swords or knives or powerfists, or mindforce(scifi magic)
You will only want to use weapons that have a Skill Increase Bonus (SI and once you have reached level 5 you will only want to use ones in which you are maxed on.
Some people get confused as to what maxed means on sib weapons. Maxed doesn't mean that you are in range, but that you are beyond it and have reached maximum efficiency.
Suppose a weapon is SIB level 5. When you are at level 4 it will say you are at 80%, this means 80% till you are at the minimum level to use it. Most weapons are maxed at 5 levels above their minimum, so you would be maxed on it at level 10.
If you look at the info window on an item, it will show you your personal stats for it considering the level you are currently at.
The 3 things you want to see are,
1. SIB = Not anymore (this means you are maxed)
2. Damage Interval 5-10/5-10 (this means you are maxed on damage, if you were not maxed it would be something like 2.5-5/5-10, or whatever the actual damage range is for that item)
3. Hit Ability 10.0/10.0 (means you are maxed on your hit ability, if your level is lower it will show something like 7.5/10.0)
It is in your best interest to always hunt in a methodical way, figure out how much ped it takes you to kill xxx number of creatures and track from hunt to hunt seeing if you can trim it down any with different strategies.
That is the start for hunting, if you prefer mining, then we can go into that as well.
edit: in response to the video above, that is NOT how I would recommend playing. If you choose to start completely for free and want to gather sweat, it is much more entertaining and social if you go where groups of people are doing it together. Though with free spawns of oil, beer, fruit, stones, etc... I am not convinced that sweating is even one of the top options anymore.
If playing for absolutely free I would recomend gathering or sweating etc... till you could buy a medical tool, then hiring out as a medic. In my opinion it is much more fun having a 'purpose' with a service than the repetition of trying to milk a few pennies alone in the corner like that.