Is the $1000 strictly for a bass, or does it need to cover an amp too? If it does include an amp, what does the amp need to be able to do - play live with a heavy rock drummer, or just at home for practice? If you need an amp to keep up with a band, I'd say you need at least 200 watts into a 1x15 or 2x10, and that's going to run you maybe $500 new or $300 used, meaning a bass in the $500-700 range. If you're only playing at home for now, you can do all right under $200 new, and have $800 for a bass. If you don't need an amp, then you've got $1000 for just the bass.
Why are you looking at the Rickenbacker? Have you tried one yet? There's no such thing as "too much" bass for a beginning player - you can learn just as easily on a $5000 boutique instrument as a $180 Squier. Maybe easier. It's just a matter of what you want and what you can afford. The thing about Ricks is that they're very particular - some people love them, some hate them. There was a whole thread here on "basses you wanted - until your played one" and Rickenbacker was the most common one named. Try before you buy - true of any bass.
Go to some stores and try stuff out. No one bass is the perfect bass, otherwise there wouldn't be so many of them. It's a matter of what suits YOU. But, some things to think about and look for:
1. Look. Don't buy a bass you think is ugly and uncool, you won't be motivated to practice.
2. Sound. Plug it into an amp and fiddle with knobs. Make sure it sounds like the bass tone in your head. Beginners needn't be too picky, but still. Some basses are a little warmer and have more "thump" in the tone; others are brighter and have more "zing" or "growl." Some have an active preamp built in, others have straight passive electronics.
3. Feel. MOST important. Some basses have thick round necks, others have skinny "fast" necks. Neither is better, just people have their preferences. There are narrower or wider string spacing, or different curvature of the fretboard, flat slab bodies or rounded body edges. Balance is important. Get the store to give you a strap. Does it hang without the neck diving for the floor? How is the weight? All this is just making sure you actually feel comfortable with your instrument.
In the $500-1000 price range, there are lots of choices. A Mexican Fender would be the standard choice - a Jazz (J) bass for a slim neck and growly tone, or a Precision (P) bass for a thicker neck and thumpier tone. You could also find a used American Fender toward the upper end of your budget ($1350 new, often used for $800-900). Among used basses, Carvins are often a great deal. They sell everything custom ($900+ new), but resale values tend to be low (because you're buying someone else's custom bass). If you stick to basic options you could order a new Carvin for under $1000. I'm also a big fan of the Yamaha BB series. High quality at a good price. They have hot passive electronics and a neck midway between Fender Js and Ps. Balance well, but a little bit heavy. A BB424x would be a great all-rounder for just about anything. Ibanez has lots of models in that price range for slim necks and active electronics.