I'm not sure what type of overdrive I want. Tube Screamer, plexi, dumble or Klon style.
The tone I have in my head is that spluttery front pick up strat sound.
I'm thinking OCD or RAT. Something right in that grey area of fuzz and overdi rve. That's the first thing I think of when I read spluttery, but it might be a little on the aggressive side.
I'm generalizing A LOT here, but if you want a smooth, clear and articulate tone, you want a Dumble or Klon style distortion/boost/overdrive. They emphasize midrange and are very smooth in character. They work well on their own through clean amps. Definitely not spluttery, IMO. Pedals like: J Rockett Dude or Archer, Ceriatone Centura, RYRA Klone, Lovepedal Zendrive.
I regard Tube Screamer type pedals as more honky, also emphasis on midrange, but to further drive tube amps into clipping. I guess you can kind of get a spluttery neck pickup Strat tone with that, but it's different than the first idea I described. To me it sounds more organic and raw if that's what you want. There's a million clones besides the Tube Screamer, but a Mini Tube Screamer would be a great start. The King of Tone I use lives (IMO) somewhere in between the Tube Screamer and the Klon camps. It's very clear, with some mid-emphasis but it can still get quite gritty.
A plexi-type distortion into a clean amp would work well too. It's sort of a similar idea as the one I described before this, just different character. I don't know any plexi-style distortions other than the Wampler offerings which are pricey.
My point is... not a point. Just get out there, listen to some demos on YouTube, pick your favorites and go try them out in a store or actually buy them and sell them if you don't like them. The latter is what I do. For me it's the only way to really see if it's working or not.