A mod is short for modification. eGo's and Rivas are kind of like production mods. They have a large battery capacity compared to the standard 510. The basic 650mah (milliamp hour) battery of the eGo will last most users 8 hours between charges, so 2 batteries will get you through the day. Just charge them at night and they're ready in the morning. I have the 900mah eGo's and I was getting 12 to 14 hours on a single battery. The Riva is basically a different brand of eGo but it has a 750mah batt. Any of the units in that class are going to give decent performance. They're kind of the standard these days.
Back to mods for a minute, most mods offer longer battery life than a standard 510 or Kr808. They don't necessarily have to be expensive, I've got some simple box mods that cost less than a Riva. One of the benefits of most mods is that they run at a slightly higher voltage. An eGo is around 3.2 volts, most mods run at 3.7 volts but you can get them all the way up to 7.4v if you want. What the extra voltage does is let the atomizer get hotter and do so more quickly. This gives more vapor, more throat hit, and the vapor is a bit warmer. The higher the voltage, the more pronounced this is. One of the reasons I quit using my eGo's is that my mod, a
Maxi Roughstack, can be used at different voltages. It also has 3000mah batteries which will last for a couple of days each if I want to go that long. It's also built of machined aluminum with no electronic circuit board so I don't have to worry about dropping it. But it is heavy compared to an eGo. Another nice thing about mods is that batteries are cheaper. Those 3000mah batteries cost $9.99 each. A replacement eGo battery is around $15 and they're about 1/3 the capacity.
As far as atomizers, the 510 is kind of becoming the standard, for better or worse. It's a good unit, but some people like other types and there's nothing wrong with the 901. 510's come in many options from low resistance to extra high resistance. You match the resistance level to the battery you have and your preferences. For a Riva or eGo you can go from 1.5 ohms resistance to around 3 ohms. The resistance level works similar to changing battery voltages. An LR at 1.7 ohms will heat up quicker and get hotter, giving more vapor than a 3 ohm one. It will also drain your battery quicker in the process. LR's have been giving problems to some eGo/Riva users in that the battery, actually the circuit board inside it, is not designed for the load an LR puts on it. Around 2.2 ohms seems to be safe, lower and you might have a problem especially if you take long draws. You can get a range of resistance levels in the 901 too, so you can customize your vaping experience using that connector as well. If you have a bunch of 901 parts on hand that might be the way to go since you could use them on the Riva 901. You can always get an adapter for a few dollars that will allow you to use them anyway though.
The basic differences between the eGo and Riva are the mah rating, the button, and price. eGo's start at 650mah and Riva's at 750mah. You can go up from there all the way to the 1300mah eGo. The higher the mah rating the bigger the battery gets though. The buttons are slightly different and some people like the softer, rounder button of the Riva over the hard plastic eGo button. Not a big deal for me. Riva's start out a bit cheaper in price, usually around $5 less for a kit. So basically they're the same, or close to it, but until you look at them both you probably won't be able to see the difference. So don't worry too much about it.
Since you're looking for more vapor and throat hit in an inexpensive unit, either the Riva or eGo will probably do well for you. I'd suggest using a 2.2 or 2.5 ohm atomizer to give it a little boost. If you're looking for even more battery life, check into one of the larger battery units like the Mega eGo.
I hope that answers most of your questions. Keep in mind that these are my opinions and others have theirs, but it's good to get as many as possible. There's lots of knowledgeable people here on ECF so just get all the information you need to make an informed decision. If you have any more questions just ask.