I've been making a living using paypal as one of my primary sources of income, the majority of my sales come through paypal.
I've had my account linked to it for a long time many, many years and years ago I was carrying a large balance there, I was marketing some very expensive office funiture there. The balance was in the 10's of thousands and never had an issue.
I will say that just like any personal and financial accounts it's always possible to worry about identity theft, and it has happened to me, (actually it was my fault as I logged into paypal once, directlly from an email, something I knew better about, but just was being careless) It was involving over $5,000 dollars and paypal handled it beautifully.
So I wouldn't be worried about the bank account thing.
There is also the paypal debit card, any of you who aren't familiar with it, it's AWESOME. You can use your funds immediately and not have to wait for the 3-5 day transfer to your account. I use it all the time. I almost never transfer the funds anymore.
You can pull money from ATMS as soon as you get them. Also, they do a cash back bonus when you use your account, and every expense I have I try and use my pp debit card, I usually can count on $50.00-150 extra bucks at the end of the month just from using the debit card for purchases.
ATM use costs like a buck and doesn't have cashback, only purchases. So I also do cashback at the checkout, this racks up the bonuses too.
Hope that helps!
Don't be afraid to connect your account, paypal is as big or bigger than most banks out there, it's as safe as anything.