Transmission on 1984 Honda Shadow 700?

Alright I just bought the bike about a week ago, for my first bike.

Now when I'm riding and shifting from 1st to 2nd the bike sometimes goes into neutral. Is this a problem i will have to address with the bike or is this just a beginner mistake?

The engine runs great, I want to keep it that way

Do you know how to shift?

The shift pattern is 1-N-2-3-4-5

Try fresh oil and consider dropping the shift lever down one spline on the shaft.

Sounds to me that you are not bringing your left foot up solid enough to shift it from 1st. To 2nd. It is a gentle shift up to shift into neutral and a solid up shift to go through all the gears.

The tranny's on all Shadow is clunky at best - most are bullet proof. There are some issues with the earlier Shadow shift forks (will pop out of third when pulling hard) but this does not sound like your problem - just put a little more toe in to the shift lever so you make it through neutral - most bikes have a bit a touch spot between 1st and 2nd (My DL1000 shifts much better if I preload the shift lever before pulling the clutch and shifting 1 to 2.
Try a good synthetic oil - often that will smooth out shifting quite dramatically (just make sure the oil weight is correct and the API label does NOT say "Energy Conserving".

Sounds like the 30year old bike is showing its age. Who ever owned it before you got you good unless they gave it to you for free. But it is a Honda so it can be fixed. Get the wrenches out and a repair book have fun.

Neutral after first gear is up so if you don't shift all the way to second it will go into neutral. I've done this before too its a simple mistake.

Shoes or Boots

Does this sound Hoakey?
Try riding a CRF450 with tennis shoes and you'll understand.
If you have to lift your foot to land first then your shifter needs adjusting or you need a fatter boot.

Neutral is between first and second gear, so it's not unusual to miss that shift. The Shadow has a fairly long lever throw so you have to be positive in your gear changes.

Your toe is just being lazy. You need to be very positive in your shifts and make sure you are moving the lever all the way through the shift before releasing the clutch.