Type-1 (symmetric pairings) are dead for curves over fields of small characteristic. Over prime fields of large prime characteristic they are not really dead, but as they only offer small embedding degrees ($k=2$), they are not really attractive from a performance point of view. You have to choose very large curves (which makes the curve arithmetic slow) such that you have a reasonable security in the multiplicative target group.
Type-3 pairings are most attractive (from the perspective of a performance and security tradeoff) as when they are used with Barreto-Naehrig (BN) curves, they have nice embedding degree of 12 (meaning that for 256 bit curve $G_1$ will give you 3072 bit in $G_T$ and this choice is ideal at the 128bit security level w.r.t. the comparable strengths proposed by NIST at the moment). Furthermore, most Type-2 protocols can be ported to the Type-3 setting by non-crucial modifications.
Type-4 are rarely used as they only are required if one requires secure hashing (in the sense that one does not know the discrete logarithm of the result to some fixed point) to $G_2$ (and that is only required rarely by protocols). As it turned out, they are also quite dangerous to use.
The different types of pairing functions $e$ (ate, optimal-ate, etc.) are basically all instantiations of the miller algorithm (aka miller loop) with different optimizations (use of distortion maps, use of Forbenius, etc. in the algorithm) and are typically restricted by the type of paring you are using.
Benn Lynn actually provides Type-3 pairings (dn - MNT curves, f - BN curves) and I have no idea why it seems that he has a preference towards Type-4 (maybe because he required them in his proposed protocols?).
I think whether they are ready for productive use is opinion-based, but AFAIK Voltage sells pairing-based crypto for years, and there are also draft standards for IEEE P1363 and I guess they will propose the use of BN curves. Also there is a draft RFC on the Optimal Ate pairing over BN curves.
Since there has been a recent progress in the discrete logarithm problem in extensions of fields of large prime characteristic (see here for a nice overview), it is not really clear at the moment how exactly this would influence BN curve choices to adjust the BN curve parameters for a given security parameter. It is thus possible that for instance KSS curves (with an embedding degree of $k=18$) get more attractive than BN curvres. So this will not really push standardization at the moment till this is clear.