My own survey ships at games start (usually conventional start) tend to be around 1.000 to 1.500t. Passives are at a bare minimum and they have no actives. Once the first couple of those get blown away, there are basicly two schools of thought.
Either go for a jump capable carrier with small, expendable survey ships. If one or more of the survey ships get wasted, the carrier usually can withdraw safely. Or go for much larger survey ships, preferably jump capbable (8.000 to 10.000t) with rather large passives and some defensive armament. The large passives usually allow the ships to spot an enemy before he spots them, so they can withdraw.
From an economical/efficiency point of view, I belive the carrier to be supperior, but I like the better survivability of the larger survey ships (I think it would be pretty hard to get crews for the "expendable" survey ships).
As for speed, well it depends on your technology. With nuclear pulse engines, my warships are around 1.600km/s, the survey ships probably at some 2.500 to 3.000km/s. With Ions, its up to 3.000+ km/s for warships and 4.500 to 5.000 km/s for scouts/surveyships. With magneto plasma drive, warships reach 5.000+ km/s and scouts 6.500+ km/s
The speed of the NPRs varies, but on contact, I usually am slower than they (again because of my conventional start) and there realy is no way around that, if your technology is less developed than theirs. You might be able to get your speed up to a level of an enemy which is one tech-level ahead of you, but the ship would probably be only engines and life support, so what would be the point?