1.0-0.5 high-sec space. If anyone attacks you there they will be flagged as a criminal, and killed by Concord (If a player with criminal flag doesn't lose his ship while in hi-sec it's considered an exploit). Note that Concord reaction time may vary and if the attacker is able to deliver enough damage before Concord arrives you will die.
0.4-0.1 low-sec space. There is no Concord in low-sec space and you are much more likely to be attacked by other pilots in low-sec. The attacker gets criminally flagged and if there are any sentry guns nearby he will be shot at by those guns. Sentry guns are present at gates and stations only. There are no sentry guns at asteroid belts, planets or moons.
0.0 null-sec space. There are no laws. Caution: there are some systems that show up as 0.0 but actually aren't null-sec space. If a system shows up as 0.0 but there are sentry guns at gates it's low-sec space with true security status slightly above 0.0 (for example Hophib in Aridia).
True security status is a number between -1.0 and 1.0. The game interface shows all systems with true SS below 0 as 0.0. For systems with positive security status only one digit after the decimal point is visible.
In systems with lower true security status you are more likely to find rats with higher bounty and better types of ore to mine.
To find out true security status of a system go to: http://eve.grismar.net/ssec/index.php
Tiers does exist, and are used to differentiate Tech1 ships from a same class. While being the same class, they fill diverse roles (mining ships, pew-pew ships), and their tier value allow you to find their exact roles (if you're to lazy to read their bonuses)...
Here is a french related forum thread, illustrating my point. (Translated! Traduction is probably innacurate, due to french being my natural langage. Feel free to edit if you see any mistakes.)
While being weak, frail, limited, frigates offset those points with unbeatable prices (always less than 300,000 isk). Because they are able to fit a few weapons, a propulsion module and / or a scrambler, they are always useful, would the pilote be a vet or a newbie, in PvP or PvE.
There are 6 variants that exist in almost any tech 2 more powerful and specialized version:
tier 1 frigates : Tormentor (A), Bantam (C), Navitas (G ) & Burst (M) are optimised for mining. They are useful only for miner apprentices before moving on to a bigger ship. They are available on the market at an unbeatable price and you receive one at the beginning of the 10 missions from the early industrialist/trader career
These frigates have no tech 2 equivalent.
tier 2 frigates : Executioner (A), Condor (C), Atron (G ) & Slasher (M) are light, fast and very affordable. By the way, their price is their only real interest, except maybe to start in PvP. One of them is given at the beginning of the 10 missions fighter career.
Tech 2 version of these vessels gives Interceptors.
tier 3 frigates : Magnate (A), Heron (C), Imicus (G ) & Probe (M) have small exploration bonuses. Note the Probe (M) which has a great bonus to cargohold which allow him to be a good small transport ship or Cyno alt. Also note the Imicus (G) is a very good offensive frigate with its drones.
Tech 2 version of these vessels gives Covert Ops.
tier 4 frigates : Crucifier (A), Griffin (C), Maulus (G ) & Vigil (M) have a greater interest, particularly in PvP. Indeed, these vessels are specialized for ewar. They are certainly far from having the power of a Recon but they can get their game on a battlefield. Note the notable exception of Vigil whose interest is not his ability but his ewar speed interceptor role.
Tech 2 version of these vessels gives EAS.
tier 5 & 6 frigates : Inquisitor & Punisher (A), Kestrel & Merlin (C), Incursus & Tristan (G ), Breacher & Rifter (M) are all fighting frigates. These are generally the best tech frigates 1 in most combat situations. Some of them are particularly good and still used by veterans.
A tier 6 frigate is given at the end of the 10 missions of the fighter career.
The tier 5 provide the foundation for SB and those of tier 6 those of AS (except for Gallente which are reversed).
The Tier value change the required commandship skills levels requirements.
The Tier value also impacts the manufacturing needs. Higher Tier ships requires more ores.
Tier values change manufacture time, BPO copy time, probability of BP invention success, etc...
I believe some more points to be also influenced, like survivability (a Punisher is sturdier than an Executionner, for exemple), or effectiveness, but i wont try to produce the whole differences list, it would take a while, and you already have the main points...
Feel free to edit my post if you think i missed something essential.
Best Answer
To strictly answer the question you asked, Osmon is sec0.7 compared to Lanngisi and Apanake which are sec0.5, meaning the concord response times are "roughly 10" resp. "19 seconds" according to this page on wiki.eveuniversity. If you can use this to your advantage and can confidently build a gank-proof rattlesnake, go there.
On the other hand, if you were to look on dotlan maps or the in-game galaxy map statistics overview by pod/player kills you'd see that (at the time of writing this answer as an example) Osmon might be the least safe system due to 4x as much traffic and 4 pod kills as opposed to none in Apanake but this does not account for faction warfare, people bullying miners, and what ever other business someone might think is a good idea to conduct.
It is also wise to look into mobile depots and figuring out how quickly you can refit yourself to maximum warp stabilizers should you get unwelcome guests (in which case the general advice is "don't shoot at yellow skulls").
All in all, the safest place to grind missions is the least convenient, your safety is ultimately an illusion, and you should always make sure that either you or someone in your crew can see a big enough picture such as map statistics (whether people are ganking missioneers), purpose of traffic and attention to local (so you can tell passers by and benign locals apart from everyone else), interceptors on d-scan, and generally just being able to gauge what business people have in your part of the galaxy.
tl;dr: There are 3 "safe" systems, as in actually in hi-sec.
I would advice Apanake simply because it has worked so well for me before but as always maybe I was just lucky.