I'll say I'm not a fan of TS type pedals with 5150's. The 5150's are already gigantic piles of mids so the TS might blow it over the top if you're not careful.
Personally I like the Boss GE-7 EQ pedal as a boost with all four of my 5150's (OG, EVH 50w 6L6, EVH 100w Stealth, EVH 100w EL34). It works as an excellent clean boost and you can get really surgical with exactly what frequencies to tweak. I like boosting 5150's at almost any gain setting and turning the amp gain slightly down to compensate because I find that kind of dialing helps push notes just a bit forward and makes the amp slightly more clear and lively sounding than with just the amp gain turned up and no boost on.
Another pedal I'd think about is an EQ for the loop. The MXR 10-band works exceptionally well with 5150's and gives you some extra flexibility in in tweaking that the amp's built-in tonestack doesn't quite reach.
Yes, I just recommended two EQ pedals, lol. But trust me, this configuration is absurdly powerful and can increase the amp's versatility by a huge amount, both in the sense that you can dial in tones and preamp gain characteristics with the GE-7 that you simply just wouldn't be able to do without it, and the MXR-10 band can make your amp fit almost any sonic footprint in which you want to place it in a mix or solo.
For another recommendation, if you want some flavor, I'd pick up a Boss DD-200 Delay pedal for the loop. It's a digital delay with the ability to dial out a lot of the treble in the repeats only (I find digital delays with tone controls the best fit for high gain amps because the repeats tend to stay clear, and when you turn down the tone, the reapeats stay out of the way). Also it has analog dry through so your dry signal is never processed. The Keeley Halo is another incredible sounding digital delay for close to the same price. And both pedals have analog dry through so they won't mess with your dry tone.
Finally, you can't go wrong with a 5150 and MXR Phase 90 for just some extra character. I like the Script models because they're more subtle than the block letter Phase 90's, and to me, subtly is the name of the game with this effect. I like to almost not even be able to tell it's on until it just tweaks your senses every now and then, that's when it's best. There are several models available, standard orange MXR Phase 90 Script, the Mini Phase 95 (it has a switchable a phase 90 mode and switchable script mode) or the MXR EVH Phase 90 that also has a script button.
You do NOT need to worry about getting the EVH Overdrive pedal with this amp. The EVH Overdrive is not meant to be a boost, it's more like an amp-in-a-box pedal to act as its own preamp going into a clean channel. It's not going to sound as good as the preamps built into the 5150 III itself.
