DnD 5e, is basically DnD lite.
It also has conversions in the DMG for modern weapons, as well as alien weapons.
5e breaks it down to its easiest form, for play.
Combat lasts about 2 to 5 rounds, and you can do several encounters a night (depending on how long you play).
We generally play from 5pm to 11pm, and we can squeez in at least 6 to 10 battles/encounters.
Anyhoo, everything you need for modern stuff is in there.
As for how things work in your world...
Determine the power level. As a new DM, you may want to go low power, in order to maintain balance and the ease of control (that doesnt mean you get to throw in your awesome big boss with HIGH POWER, and totally wreck the heroes...lol, but you can push them to the limit :-) ).
Magic can be a rare commodity, and sought after. If you have a player that wants to play a magic user, you can say hes one of the few who has studied, and most people dont even believe that magic exists. So, you force the hero to be careful not to cast magic out in the open, for fear of being branded as a heratic or a witch.
Then, that can create an antagonist for a plot hook. A wizard slayer is seeking him out to exttact his ability to perform magic. (Or whatever).
Youll do fine, just be confident, plan, and set your ground rules at the beginning of your campaign. Ie...houserules on things that you will make rulings on. ie..how you want death to work, casting into melee, or anything else you want to rule on (if certain rules are unclear).
Its your world, bring it to life, and let it roll :-)