Welcome back, your timing is impeccable. Remember how crappy a $2-300 bass used to be? Not anymore! It's amazing what you can get for short money now. IMHO, the best bang for your buck in virtually every price range is Ibanez. They run in ascending series, SR200, 300, 400, etc. The 200 line is an entry level bass, starting at 300 and 400 series are all any amateur bedroom bassist (like me) will ever need. The SR 500 series is pro-level, anything beyond that just gets prettier cosmetically, incremental improvement in hardware and electronics as you walk up the line. The top of the line Prestige series are boutique-level instruments for around $2000 and up. They are all light, ergonomically superior, and have a very thin, fast neck, so not great for the ham-fisted, but very comfortable for small to normal sized hands. The higher end models have Nordstrum pups, the mid-range have Barts, great sounding either way. Excellent electronics setup, with Master Volume, Pup blend, and three-band EQ, passive or active. If I was in your shoes, I'd get an Ibanez, no question.
Another bass line to check out is the Squier CV and VM series, excellent basses for the price if you prefer a Fender look and feel. I think they are equal to most MIM Fenders, opinions vary hugely on this, of course. Speaking of Mick Karn, the Squier VM Jazz Fretless is a great bass, it's a lined fretless "ebanol" (phenolic) fretboard, no pickguard like a Jaco Jazz, instant "mwah" for cheap.
The Sire line by Marcus Miller also gets a lot of love around here, though I haven't tried one personally.
For amps, you are also in luck. Most amps these days have an aux in and headphone out for playing along with MP3's or CD's. The Fender Rumble 15 is very well reviewed, my son has Rumble 30, and it's more than loud enough for church and coffee-house sized gigs, the 15 would be plenty for bedroom use. There are also plenty of high quality headphone amps, some with effects built in, ability to mix with other music sources for playalong, software to slow down and pitch correct music for learning, etc, all of it relatively cheap!