Well, you have two different things going on: Solid vs. Hydraulic, and Flat Tappet vs. Roller.
Basically, with a solid lifter, you need to adjust for wear every so many miles by adjusting the lash. That, and they make a bit of noise. So, manufacturers went over to hydraulic lifters, which use a tiny hydraulic piston to adjust for wear. Since they are always adjusted, and due to the spring of the oil in the lifter, they make less noise. Solid lifters, however, are more tolerant of high-rpm use.
You also have to consider how the lifter is connected to the cam. Flat tappet lifters have a flat face that slides across the cam. The cam lobes have a slight bevel to them, which causes the lifter to rotate as it does this, helping them last longer (the wear gets spread out by the rotation, instead of happening all in the same place). Roller lifters are just that: they have a roller on the end which rides on the cam. This results in much less friction (every hp counts) and, due to the geometry, allows a more agressive cam profile to be used (a roller lifter can open and close more quickly than a flat tappet lifter). The roller lifter doesn't rotate like the flat tappet. Actually, rotation would be a major problem, since the roller would not line up correctly, so there needs to be some device to keep the lifters aligned. Newer blocks are set up for roller lifters, from the factory. Older blocks must be converted, which can cost a bit of money.
So, with these four types of lifters, you have four types of cams. Most importantly, is roller vs. flat tappet, since the cams are ground differently. The slight bevel that is necessary for a flat tappet, is incompatible with rollers. Solid vs. hydraulic is more a matter of profile: you can use solid lifters with a hydralic cam, but a cam that is listed for solid lifters is probably listed that way because its profile is too agressive for use with hydraulic lifters.
In terms of "which is best?" it depends. For most of us, flat tappet, hydraulic lifters are all that we need. When you start to push the performance more, it may become necessary to switch to hydraulic roller lifters (and a cam to match), due to the more agressive profile that is possible. Extreme performance may require solid roller lifters, but that's probably beyond the level that most of us will deal with.
I left out solid flat tappet lifters, 'cause personally, if I'm going to have to deal with setting lash, I'm going to do it because I passed the point that hydralic rollers allow for. If the performance level is not high enough to require solid roller lifters, then I'd rather have the convenience of hydralic rollers.
So, in your car, if you just want to drop in a new cam, you're going to be looking for hydraulic, flat tappet cams (and lifters - you need to replace the lifters whenever you put a new cam in - it usually voids the cam warranty if you don't). Unless you feel like spending a few extra bucks and getting hydraulic rollers.
Joe