Thanks! Don't worry about the tube getting hot. Just turn it off when you're not listening.
Unfortunately, you won't be able to connect the turntable directly to your amp. When they make records, they apply the RIAA curve to them. There are a lot of technical reasons for this (you can look them up if you want), but it cuts out a lot of the low end. If the bass were accurately represented, it would make the grooves a lot bigger, making the amount of timme the record would play a lot shorter. So you need a phono stage to put the missing information back in. It's sort of like an equalizer at a fixed value. You can spend whatever you want on a phono stage, but you can find decent ones around $30 at Garage-a-Records. If you want to spend a little more, the NAD PP2 is pretty good - I used to use one before I got deeply into tubes.