I think that's a question you really have to answer, not us.
If your question is, "What's the least I need to spend to comfortably accomplish these goals" then $1000 is probably fine, since it sounds like you already have a monitor. That $1000-1200 range is sort of the sweet spot in terms of price/performance.
You can do it for less than $1000, but you start having to make compromises.
You can certainly spend more than $1200 and buy higher-end parts, but it's not strictly necessary. Some people do enjoy that though. That's why I say whether or not it's worth the extra investment is really a question you have to answer for yourself.
Edit: And if you do decide to spend over $1200 I would look into upgrading your monitor.