I've been playing bass for 12 years, and in my experience, unless you're playing a few times a week or just doodling around, cheap basses are the worst you can get.
Get something a bit better. The new Suiqer "Vintage/Classic Vibe" series basses can be had for under $300 and sound REALLY nice. They also play and feel great too.
If you just want to jam with your dad and don't really care about how your tone sounds, then either of those will be fine.
If you are serious about playing, I'd suggest getting something of mid-high, or high quality off the bat. I've put a lot of money/effort into getting a defined tone, and I can tell you that it was worth every penny.
Split-coil, also know as "p-bass style" pickups give a great sound. They have lots of growl and vibe to them, great for playing with a pick if you choose to. Jazz-style pickups aren't split like the p-style, but also sound great and usually come in pairs. These pickups are often more mellow and have less bottom-end (bass) than a split-coil will have. My P-Bass special has one of each. A bass like this can allow you to open your tonal pallet and explore what kind of tone sounds best to you. I personally never use the jazz-style pickup, because it's too thin sounding, and because it's in the bridge position.
In regards to active/passive, it really comes down to the sound you're looking for. I wouldn't recommend active if you're just messing around. They aren't "battery-sucking monsters." My old Peavey Rudy Sarzo bass had an active preamp and I changed the battery maybe once or twice a year during heavy gigging. This also depends on the pickups/electronics used inside.
The best thing to do is go to a Guitar Center, or a local music shop and try some stuff out. You could even play 7 copies of the SAME model bass/guitar and it could sound completely different. Play a lot of different models and different brands of basses and get what sounds good to YOUR ears. If you like the way it sounds, then there's no need to worry about what any one else says.
Good luck!