My advice would be to go for the most powerful system you can afford, even if it's more than you currently need, as you'll likely grow into it soon enough. But there's no simple, single answer. A Porsche might corner and brake faster, but it can't pull stumps or haul lumber like an F150.
You don't really need a very powerful system just for tracking (recording) 16 tracks of audio. A netbook or iPad can do that. But if you want to record at high sample rates or throw any fx on the inputs while tracking or mixing, that requires more cpu power. And softsynths also use more cpu power and can benefit from more system memory for samples.
Video editing isn't necessarily demanding, and the on-core HD4000 graphics on the latest Intel "Ivy Bridge" i5 and i7 cpu's can handle that at even high def resolutions, so you could get by with using the onboard graphics, or a lower end graphics card. Your 40" TV probably has an HDMI input, so a motherboard or graphics card with an HDMI port would be necessary (but you need to confirm what input jacks your display has, in order to know what you'll need!).
For a basic DAW, you'd probably be looking at an i5 Ivy Bridge cpu (4 cores, 2-channel memory support, no hyper-threading) with 8 GBs or more of memory. For more power you'll want an i7 Ivy Bridge cpu (4-cores with 2-channel memory support and hyper-threading) and 16 GBs or more of memory. Either of these cpu types would use a "socket 1155" motherboard with an Ivy Bridge chipset (PCH) With a "K" cpu such as i5-3570K or i7-3770K and a Z77 or Z75 motherboard you would have the ability to "overclock" the cpu for more performance.
Next step up, at quite higher cost, would be an i7 Sandy Bridge-E cpu on a socket 2011 X79 motherboard, starting with the i7-3820 (4 cores w/hyperthreading and 4-channel memory support) or i7-3930K (6 cores w/hyperthreading, 4-channel memory and overclocking support) and 16GBs or more of memory. With such a system you'd have plenty of power for most any DAW needs (could cormer fast, pull stumps and haul lumber). But you'd also need to install a separate graphics card as these cpu's do not have onboard graphics.
You can install a PCIe (PCI Express) Firewire adapter with T.I. or LSI chip, so don't worry about onboard Firewire support on a motherboard.
You'll also need storage drives for your operating system and DAW applications and audio data, samples, etc. Solid state drives (SSDs) are fastest but are lower capacity and highest cost per GB compared to hard disk drives (HDDs).
You'll also need a power supply and case, and may want or need a good quiet cpu cooler.
If you have no time or are not computer/DAW savvy, then it might be wise to consult a pro system builder who could (possibly for a fee) give detailed recommendations on a system to meet your specific requirements, and who could also build a custom system for you tailored and tuned to your specific needs and provide support down the line.