Bass and pro workup - 300
100 watt amp with a PA system output - 300
Some cables, tuner, and nice strap - 100
You're in it for 700. Take the other 300 and put into lessons after you've learned the basics and a couple songs when you hit a progress plateau.
Here are a couple low-end used basses (low-end but very usable / playable / gigable) for under $200. 2 Ibanez, a Yamaha, a jackson, and a Mitchell. 2 are short scale (one 28ish and the other 30ish) and the rest are full scale. Add in a professional tune up and strings, you're looking at less than $300.
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Mitchell MB100 Short Scale Solid Body Electric Bass
Get a Fender Rumble 100 amp for $300 (used amps are harder for me to come by)