1k is pretty tight for a 5 channel upgrade, if you could go to 1.5k you'd be a the best shape. However that said 1k can work. Speakers are a tough call as there are so many decent choices at this price range. Here's what I'd recommend specification wise and maybe you can talk to your shop and ask them what brands they carry and would recommend.
Also does that 1k include installation or are you budgeting extra for that (which would be a good thing)?
- Amp: 5 channel Alpine PDX V9. This is an awesome amp for a single amp install to run front stage (midbass and tweeters). The most expensive part here but the best investment imo. About $500. I bought all my amps off Amazon via Prime so I could return them if there's any issues and you'll save a bunch of a custom shops price.
- Dash mid/tweets: You'll want to find a good full range 3 inch speaker that will do a good job at about 280hz to 18k. I'd suggest Hybrid Audio L3SE but they are overly pricey
See what your shop has to offer.
- Doors: 6.5 inch midbass.
- Sub: If you don't want to pay to have a box built then you should consider going with a prebuilt box/sub kit. JL has some good products in this area. Won't be pretty (ie it won't be fully integrated into the interior) but it will perform MUCH better than the factory sub ever will. The factory sub is trash.
All in all what I am suggesting is a 5 channel amp running the front dash, doors and sub. You might even consider turning off the rears and center channel bose speakers altogether but that is up to you.
Later on budget permitting it would be very helpful to add a processor as this is the one piece that can have the most dramatic effect on sound quality in the car as tuning is definitely necessary but very difficult without a processor.
I'll do some research with my contacts and see if they have suggested brands/models in your price range.