Most of the finnesse techniques you stated, mainly the plastics, would be more effectivley fished with faster action rods. The softer tip would allow for better castability of lighter baits, but the backbone would still drive single point hooks home. However, for small cranks and spoons, you need a more parabolic rod, Moderate-fast to moderate action. To achieve this, and still have a softer tip and the backbone, add length to the rod and reduce power. This gives better shock absorption throughout the rod and your trebles wont come ripping out.
There is a lot of confusion about the proper rod for jerkbaits, but a fast action rod is better to achieve good action, and for shock absorption some companies keep the power around M-MH, and add length to the rod, and some companies keep the rod shorter but reduce power to M-ML.
In your case, a rod that is ML/M power, and 7'-7'6" in length with a fast action would be proper. The fast action will give you good sensitivity, and good lure control for your plastics and jerks. The longer and lighter blank will help absorb shock on your small cranks, and other treble hook lures.
Finding a rod like this is difficult for casting, but there are a lot more finesse technique rods in spinning. I would go for spinning with braid 100%. You get better distance and castability, and I find that with light rod and baits, its more comfortable to hold a spinning rod. I guess its just preference.
For being a more "modern rod", you will be looking for the material, and nowadays, how its constructed. Higher mod graphite will give you that light, sensitive, and crisp feel. I suggest looking at Daiwa rods with X45 and either HVF or SVF. The Tatula rods are incredibly light and sensitive at a good price. They are slightly above $150, but you get quality components and a quality blank, and comfort. The TTU711MLFS model will be a good bet for your needs, but a TTU761MLMFS would probably be best (slightly longer, slightly heavier). They are aimed more for dropshot and float'n'nfly, but I never look at what a rod is labeled with-I look for the power action length (PAL) combo that I need. I currently have 3 Tatula rods and so far this PAL selection method has not disappointed. All my rods are perfectly suited for my needs.
If you want something more budget, Lamiglas offers a rod around $90, the XP Bass Series. The XP702S is a general purpose light duty spinning rod that should cover the techniques well. A slightly heavier XP703C is a casting rod as you are looking for, and instead of being a bit longer to increase shock absorption since its a heavier blank, they made it a mod-fast. This should work well for weighted plastics, but not too confident in weightless. Again, more choices in spinning rods.
Good luck in your search!