Build your own computer. If you don't have these skills, I'm sure someone in your field does, and you should pick their brains so you have them. As a programmer you should build this knowledge anyway. For reference, my computer easily handles Skyrim at near to highest resolution with many other programs left open in the background. It also does the mmorpgs I play at highest resolutions with no issues whatsoever. My SO helped me pick out parts and the total cost for the case and everything inside it was ~350. Unless you are doing serious rendering, I'd guess that you don't need a lot of the stuff a $1000 budget allows when you're building your own computer. I will allow you a better graphics card than mine (you want skyrim at highest resolution, with ALL of the prettiest mods). I will also pretend that you are all about the pretty in real life in addition to the virtual world, so your case will cost more than mine. You also like to compile code at tremendous speeds, and need extra memory for your extensive library of 100% legally obtained music and video content. $600. Go forth and conquer newegg. You should come back and tell us what your 'this would gracefully handle all of the things I need to do on this computer' components would cost if you bought them as parts, then your 'oh my god, i never knew such a beautiful thing could be mine' list. People on this board more technologically versed than myself will probably be able to help.
Check out your local thrift stores or craigslist for cheap peripherals. I got my first monitor for $15 the first time I walked into a thrift store looking for one. Also check with people you know if their company switched computers recently. This is how I got another monitor and a set of speakers for computer screen movie nights.
Have fun on the keyboard front, having the same type is understandable and related to your productivity at large. Even so, this shouldn't cost you more than $125, and that's if you're going with led backlit insertcolor cherry switch mechanical monsters. Did your work buy you one of those?
A mouse that doesn't double click when you click once? Are you sure you don't mean 10 programmable buttons and custom lighting? The former will cost you $15 MAX on amazon. The latter is not necessary. Unless it is. But you should think about why if you really feel that's the case. Do you play LoL professionally? Can I stream your games on twitch?
And yes, definitely save for the computer. Please don't buy it on credit. That's a terrible precedent to set for yourself just starting out with your (presumably) first salary.
Also, I mean all these questions and suggestions in good humor, and to offer alternatives to standard retail problem (want a thing>buy it full price>don't learn from the want in any way). These are the same types of questions I ask my tech head roommates every time one of them wants a shiny thing. In any case, enjoy your gig and congrats on the degree!