Videocards
Both Geforce and AMD have solid offerings at the moment, but GeForce is probably a better bet due to Radeon products being better at Litecoin and other cryptocurrency mining. Radeon pricing is all messed up because of the intense demand for mining.
For AMD, the best cards start at the R9 270 and higher. For GeForce, the 760 and higher.
The best $300 card at the moment is probably the Geforce 770, which was a re-released 680, their prior top of the line model.
The Radeon R9 280x is equivalent however its pricing is out of wack because of the mining. This is a re-released version of the Radeon 7970.
The current top of the line cards are Nvidia Geforce 780Ti and AMD Radeon R9 290x.
Videocard drivers are finally at parity between both Nvidia and Radeon, and Crossfire's stutter issues have been greatly resolved so it is competitive with SLI.
Videocard's have a "turbo" mode now, called boost. Cards focus on a particular temperature and try to maintain a boost frequency to stay at or below that temperature target.
CPUs
AMD has fallen out of the high performance processor segment and focused on APUs, medium powered CPUs with powerful integrated graphics built in. The best performing AMD at the moment are the 8 core 8320/8350/9370/9590 processors on socket AM3+, which unfortunately lack the integrated graphics of AMD's APU line up. It is likely that AM3+ will be discontinued.
The current APU architecture is Kaveri which runs on socket FM2+, which is the first solid contender from AMD for the APU market. Kaveri can hybrid crossfire its built in "video card" with the discrete radeon card, the R7 250 and 240. Sadly you cannot crossfire it with the R9 series.
AMD has released the Mantle API which is a competitor to Direct X and Open GL. Because AMD provides components for both the PS4 and XBoxOne, Mantle could be significant but it is too early to tell. Under Mantle, AMD products should perform much better than Intel and Nvidia products. There aren't very many games that run under Mantle at the moment. It is unclear if it will be widely accepted. AMD uses modules with its current line up, each module has 2 integer cores and 1 floating point core. The 8 core FX processor therefore has 8 integer cores and 4 floating point cores. This has a slight performance penalty between an FX core and a comparative Intel core. Most games presently only use 1 or 2 threads. Therefore Intel CPUs are usually better at games, but not significantly. AMD's FX chips are very cheap and provide a lot of multithreaded performance for the price. If you are using applications that use more than 4 cores, AMD is probably the way to go.
The current Intel model architecture is Haswell (socket 1150), which is very similar to its predecessors, Sandy and Ivy Bridge (socket 1155), maybe only about 5-10% faster at the most, but with a better integrated memory controller (faster ram options) and better integrated graphics. Intel's HD Graphics don't really compare to AMD's integrated. Core i5 models have 4 cores and 4 threads. Core i7 have 4 cores and 8 threads by means of hyperthreading. Core i5 and i7 are virtually the same performance with gaming, but the i7 has a lot of advantages for productivity in areas such as video compiling. Intel's cores are much faster than AMD's cores. Intel is pricier. If you play games that require a lot of single threaded performance such as Starcraft 2, WoW, and Total War, Intel is the way to go.
Ram
DDR3 is the current standard but DDR4 will come out in a year or so. Not sure if there will be any performance improvement with DDR4. 8GB is the current recommended ram amount. Ram prices have risen greatly since 2012 and ram is probably very overpriced at the moment.