The SR225/225i is great with Fiio E11 on Bass Boost Level 1, I don't know about the E17 but I would guess it's more or less on the same level with E11 amp-wise. Otherwise, if you want to try tube, you may look into hybrid amps first since they are often cheaper and fairly easier to maintain. My Grados have great synergy with the original Millett Hybrid, Little Dot I+ is also often recommended (I have not tried it myself).
Well I am listening to my 225i on my HiFiman EF2a as I type this. Tube amp/dac and it sounds very good to me. For less than $200 your choices are very limited. Audioengine makes a D1 amp/dac that has gotten some good reviews as well and it is under $200. It is solid-state but at this price level I don't think it is going to make a big difference, tube or SS.
You may want to look into the amp output voltage. The LD MKIII is designed for high impedance cans whereas LD MKI+ is for low impedance. SR225i is rated 32 ohm only so I don't think the MKIII is a better tube choice for Grado despite its higher price tag. Don't know about the other two amps you mentioned though. And I do notice a difference between tube/hybrid vs solid state even in the sub-$200 price range, especially some improvement in the bass and more pleasant overall tonality when using the SR225 with my Millet Hybrid compared to my Audio GD dac/amp combo.