Forgive me if its a stupid question. What processer would one choose if he is ultra low in budget and wants to play semi-modern games as his main purpose. the graphics card a old HD 5450. Yeah i know...i know....... Games preferred are Prototype/COD4/COD6/Crysis/Farcry2/Halflife2and games of that period.
The Radeon HD 5450 is a relatively old card. AMD and Intel APUs/CPUs have integrated graphic cores that are more powerful than the Radeon HD 5450.
Intel's Core i3-3225 is a dual core CPU with the Intel HD 4000. It is just slightly less powerful than a desktop Radeon HD 5550 graphics card. Note that all Core i3 CPUs with models ending with a "0" will have the slower Intel HD 2500 graphics core which is slower than the Radeon HD 5450 so for those models you will want to use the Radeon HD 5450. The i3-3220 is an example of a CPU with the HD 2500 graphics core.
AMD's Trinity APUs also have graphic cores that are more powerful than the Radeon HD 5450. The A6-5400k has an integrated Radeon HD 7540D and it is basically as powerful as the Intel HD 4000. The "k" means this CPU can be overclocked. There's also the A8-5600k with the Radeon HD 7560D and the A10-5800k with the even faster Radeon HD 7660D graphics core. The HD 7660D's performance is basically between the desktop Radeon HD 5570 and Radeon HD 6570.
Of all the processors mentioned above, the AMD A6-5400k is the least expensive; it should cost roughly $75 - $80. The Intel Core i3-3225 will likely cost about $130 - $135. While the graphics cores are roughly equal, the i3 CPU core is definitely more powerful despite having a lower clockspeed than the AMD APU. Most games are limited by the graphics core rather than the CPU. If you were to play Crysis 2 then you should find that the performance between the A6 and i3 will be very similar. However, some games likes both powerful CPU and GPU such as Skyrim. The Core i3 will provide better performance because of the more powerful CPU.
The A10-5800k costs almost as much as the Core i3-3225; roughly $130. Basically speaking the A10 would be the better choice no only because of the faster graphics core, but also because it is a quad core CPU (APU) that can be overclocked.
The A8-5600k is sort of like a good all rounder. Since it is a quad core APU, the graphics core is more powerful than the Intel HD 4000, it is overclockable and it should be priced at around $110. However, unless an extra $20 is considered a lot of money, the A8-5800k is the better deal.
The Core i3-3225 would be the CPU to buy if you (or your friend) definitely plan to install a graphics card in the feature that is faster than a Radeon HD 6670. The AMD APU have something called Dual Graphics which allows you to install any Radeon HD 6xxx up to the Radeon HD 6670 and it's performance will be combined with the integrated graphics core to provide better performance than the Radeon HD 6670 can provide on it's own. I do not believe the Radeon HD 5xxx and 7xxxx series graphics cards are supported in a "dual graphics" setup. nVidia cards are absolutely not supported by "dual graphics".