Hi aeronine!
With a toon that is level 60, the drops you can get will be mkXII (with the exception of a few mkXIII you´ve already mentioned).
Also, the highest mk level, that you can craft, is XII. But I wouldn´t recommend that anyway. If you´re deciding to craft weapons (or other stuff), then go for mkII (yes, 2!) and upgrade the items from there. *)
The reason for it is: it´s cheaper. You don´t want to craft a mkXII item with crappy mods (which you can´t choose, btw). Just craft mkII until you´ll get the right mods and proceed from there. Sell the rest to a vendor or trash them.
*) There are a few exceptions: omni-beams, for example, are only craftable as mkXII.
How to upgrade stuff
If you look at your inventory, there´s an upgrade button at the bottom left. Click on it and the upgrade window will open. Left click and drag the item into the upgrade window. You can also right click on the item in your inventory.
[attachment=3231]UpgradeStuffLines.jpg[/attachment]
You also need tech upgrades. They come in different flavours, but I´d recommend the superior ones - you´ll need fewer dilithium in the end. Tech upgrades can be either purchased on the exchange, at vendors (except the purple ones) or you can craft them in your schools. Superior ones require your R&D school to be on level 15 (rare level 10, uncommon level 5).
Check the window, it´ll tell you how many tech points are needed to get to the next level - or hopefully (gambling warning, just saying) to a higher rarity of the item - and how many points are provided by the tech upgrade you´ve slotted.
To be honest, if you´re patient, then the better way is to just craft superior tech upgrades and sell them on the exchange. With the earned ec you can then just buy the stuff you want. I would only upgrade items which can´t be bought, like... no idea, embassy sci consoles, spire tac consoles or reputation gear.
I hope that helps?
Greetings, A.M. :)
Edit: I´ve found this (you have to scroll down):
https://ufplanets.com/showthread.php?51270-Guide-Epic-GearI hope it helps you to decide if upgrading an item is worth it. :)