Don’t dismiss the possibility of a small head with a cab. I have a GK 300 watt head (weight about 3 pounds) that is clean for the small to medium gigs I play. I have a Euphonics Audio Wizzy 10 (10 inch speaker, weight about 11 lbs). This works great for small gigs or gigs w/o drummer, total weight is about 15 pounds. I never need more power, but if I do need more volume I can plug into the house PA (and use this rig as a monitor). It is a bit more trouble than a combo amp, but very flexible. Use the EA cab with a guitar amp (great clean tone), or use the GK amp with a larger cab. Easy on the back great clean tone and takes pedals well. I have had this rig for about 10 years now. The Wizzy isn’t made anymore and there are higher watt amps now in smaller packages. This rig is fabulous for home practice. If I had thought to get a 12" speaker cab at the time, it would be the only speaker I would ever need to own for bass or guitar.
i have always believed that between 250-500W is the perfect sized amp for most people, 300W will do the job just fine.
Resurrecting an older thread eh? Oh hell, now I’m doing it.
For those who might be looking in for the very first time my suggestion is to think about how you will eventually be using the amp. A little planning ahead can save you money. If you never plan to use a rig outside of your home or to jam with some friends at acceptable in home volume a 50w-100w combo amp will do just fine.
But…if you’re gonna do any gigging or jams with it where there will be a full band with a potentially loud drummer and loud guitars than @itsratso is spot on. You should be looking at a rig that will produce at least 250-300w minimum. Look around at barely used quality gear. That should save you some money.
Buying too little for your eventual needs means selling that smaller amp at a loss then having to turn around and buy something more suitable for your needs. Even if you don’t need 300w plus immediately that why all amps have a volume pot. Turn it down. I’ve played 750w rigs in a 3rd floor apartment without a single complaint.
When going with a more powerful rig buying a separate head and cab will always give you more flexibility than a combo. It will typically weight less as well. I’d start with single 12" cab and add to that if needs change. There’s a ton of very good gear to choose from both new and used so play some of it and fine one that fits you.
i put a longer explanation before in another thread, but the tl:dr version:
double your 250W amp to 500W and you get an extra 3 db loudness. how much is that? it is commonly said that 3 db is the minimum increase that most people can easily hear. so it’s “a little louder”. this is the formula, double the watts equals 3 db more. to make your amp twice as loud you need an extra 10 db. (ie adding 10 db makes your amp sound subjectively “twice as loud”). so you would need 2000W if you started at 250W. amps have a ridiculous amount of diminishing returns. good news, save your money (and maybe your back) and buy a smaller amp.
Yup, it’s more about the added head room you get by increasing the wattage which in a bass rig is important but there are other factors involved as well. One would be playing through a more efficient/sensitive speaker. A speaker with 103dB sensitivity is 6dB more than one producing 97dB. That much difference will produce a more noticeable amount of volume.
Multiple speakers (2) running at 4 ohms as opposed to a single 8 ohm speaker can also be more efficient by using all of the amps potential output. More cone area will also help to produce a full sound and greater perception of audible volume. Just some other factors involved in deciding what to buy.
My take on this for a new player is to get a decent size amp with decent volume. This is a multifold answer.
One, you don’t know what you don’t know. Regardless of how much you do your research on your first bass or amp, you won’t know if you like it until you are actually using it. It gets more complicated when you actually have to use it in a Jamming environment.
Two, your taste will change over time. Oh! it will.
Three, your budget will change over time, once you are a self proclaimed bass player you’ll look at gears differently and your commitment to gear will change. You’ll be able to spend more on things your are Enthused about, 
When you are ready to spend $1000+ on an amp, by that time you’ll know what camp you want to be in and what Flag to fly.
So my usual, advice to the first time amp buyer is to get what you need now with a little head room for near future. Quiet enough to practice at home while everyone is sleeping with good tone, and can be loud enough to Jam with a drummer when they are you to join their “Super Group”. If you are super lucky and get to gig sooner than you can get bigger amp, there’s always the mic option to the House PA.
Worry about later, later!
I have a Fender Rumble 100 that I’ve used to practice and used to use it to jam with some friends. I’ve got a larger amp too mostly for enjoyment at home/when I end up in a band of some kind again one day. The Rumble is plenty light and sounds good to my ears.
For practice I’m currently plugging in to an interface and using headphones, but I also have young ones at home and need to practice in the evenings. On weekends it feels nice to get the amps out and get some volume going. Even with a much larger amp I like more available I’m still fond enough of the Rumble to keep it. It’s just super convenient to use and can grab and go for an acoustic jam.