
Which skills will I need to make the most of out the mining experience.
This depends largely on where you want to mine. If you aren't ever planning on leaving HiSec I reccomend getting Exhumers to at least 4 and Mining Frigs to 3. That will get you comfortably into Skiffs, Makinaws, and Hulks.
In addition to this Refining to 5 and Refinery Efficiency to at least 3 if you are staying in HiSec. Then the applicable Ore Processing Skills to IV. In Hi Sec you will find Veldspar, Scordite, Pyroxeres, and the regional Kernite, Plagioclase, and Omber. these Skills are what will get you the T2 Crystals in the T2 Modulated Strip Miners.
I also strongly recommend All the Rank 1 Skills to V. Engineering CPU Management, etc. Core Competency Standard would be a good Certificate to this end. Drones to V, Scout Drones to V, Active AND Passive Shield Tanking to Standard.
In Hisec your ships should be able to tank the belt rats until the cows come home with those skills so you can use mining drones to increase yield.
You will want Mining Upgrades to IV as well. That will get you T2 Mining Laser Upgrades. That also answers your second questions. Those go in Low Slots.

Should I stick with +4 implants or take the time to train to +5? I've read about foreman links, but do they work for a solo miner?
The Mining Foreman Links don't help you personally much but there are refining and Mining Yield implants that do Benifit from having Cybernetics V.

What would be the best solo mining ship? And if mining with a group does it change anything?
There isn't really a best "SOLO" Mining ship. The Procuror/Skiff can be heavily Shield Tanked which makes them a pain in the ass to gank. Gankers generally won't try. They will move on to a softer target.
The Retriever/Makinaw have very large ore holds, so I guess that as a solo miner this will be your first choice of ship as you can make slightly more in it without a hauler than you can in a Hulk.
The Covetor/Hulk are the pure yield ships, however to benefit from this you need a dedicated hauler. Another drawback here is that both the Skiffs and Mackinaws have more ability to tank. Though you will still have no issue with NPC rats in these.

Should I stick with one system and one kind of ore during my mining career ? if not where can I find different kind of ores to mine?
Find an area of Eve you like. The actual system doesn't matter though the Sec Status does. 1.0-0.7 will be the safest, while you will start to see occasional ganking in 0.6, and more frequent in 0.5 systems. Actual ore types as listed about you will find in HiSec. Once you decide to move to Null Sec you will want Refinery Efficiency 5 and the rest of the Ore Processing skills.

If I want to branch out much later on into refining/manufacturing/transportation/trading (I realize this will take a long time but i'm willing to invest in it) how should I start with this, do I mine and keep all the ore I will amass for later use?
This is really a question for its own post but the short answer here, is Production Efficiency 5 and Mass Production 5.