From what it sounds like, all you might really need is a basic processor. Even the slowest Pentium of the latest generation could handle all these needs. But I'd recommend these i3 models for some headroom:
i3-4150 - 3.5 GHz (~$120): Best bang for the buck of the i3's, slightly slower graphics clock speed and clock speed than top i3.
i3-4360 - 3.7 GHz (~$150): Fastest i3. Has more cache than the 4150. Not as worth it since the cheapest i5 costs only $35-40 more.
But if you are going to be doing some big calculations in your work, you might want to step it up to at least an i5.
i5-4460 (3.2 GHz, 3.4 GHz Turbo) (~$185): Cheapest i5. Only worse in clock speed compared to the faster ones.
i5-4590 (3.3 GHz, 3.7 GHz Turbo) (~$195): Best performance-price ratio of the i5's.
i5-4690 (3.5 GHz, 3.9 GHz Turbo) (~$220): Fastest i5. Comes in an overclockable version for about another $20. I don't think this is the best choice for you since another 200MHz is not much for $25 more, but it's here for reference.
Core i7's will work, but cost just over $300 and may be overkill for what you want to do.
I'm not very familiar with AMD processors, but someone else could handle that. Ask me if you have any questions.