In my suggestion,
Don't buy an iPad, instead buy an iPhone6+, why?
You can use it as phone even when you're not doing a test. If an app running well (in most cases) will run on iPad (except some UI objects which you can easily test in simulator). This seems funny but you will happy with 6+.
Even you can buy iPod 5th generation. Which are little cheap.
No developer account? Not need.
If you've a device then ask your friend (who have iOS developer account) to add your UDID into their account and grab you provisioning profile and certificate. For a registered account one can add 100 devices. Mostly they don't have this much of devices. If you're a good friend then he may not say NO. Even you can offer him for a treat (a beer or coffee) for this.
No good friend / No Device ? Still don't worry.
Either you can purchase a device (which you want) and open-up a account, and Yes you'll be happy forever (at least for a year, you've to repay after one year).
OR
There're several online testing services from which you can choose the best for you. Mostly they will charge in minutes they test your app. I seen one service which give 200 minutes/month @ $20 (or 1200 minutes/month @ $100). For a very small app this can be enough (after proper unit testing in simulator by you).
At last,
Having a device and account will be a long time investment. If you have both you can test and upload (your own apps too) on AppStore. But at minimum investment cost of $700 to 800 .