The Uniden 520 is a great choice for a basic radio. I've been using one for years with excellent results. It's really hard to beat for the size/money.
Consider the K30 magnet mount antenna for an alternative in that size.
I've used both it and the Little Wil and found the K30 to perform noticeably better. It's also less expensive:
The other commenter that suggested getting an SWR meter is also correct. These antennas all require some degree of adjustment for optimal performance. Just a basic meter will work fine.
And the jumper: http://www.amazon.com/Procomm-Coaxial-Cable-Jumper-Connectors/dp/B003DRJ738/ref=pd_bxgy_auto_text_y
The meter and jumper is something you'll very rarely need (just when moving the setup to a different vehicle, for the most part) so if you husband has a friend into CB or HAM operation, he may be able to borrow one for a few minutes rather than buying.
Finally, you'll need some way to power the radio. The easiest way is with a lighter plug: http://www.amazon.com/Roadpro-Fused-Replacement-Cigarette-Lighter/dp/B0016LG0CY/ref=sr_1_1?ie=UTF8&qid=1417901045&sr=8-1&keywords=lighter+plug
Just cut the connectors off the ends of the wires and splice it with the ones on the radio.
Alternatively, you can connect to the fuse box with an Add-A-Circuit. These come in different sizes depending on the fuses in your car. You can get one of these for less than $10 at any auto parts store.
Looks like you're missing a few things to get it up and running. I'll link what I think you'll need below, and provide the cheapest/best stuff for an entry level rig.
You'll need a 12V power supply if you plan on running it from home as a "base". Here is one on Amazon for $31.00
https://www.amazon.com/dp/B0002BA570/ref=cm_sw_r_apa_i_GjrFEb2QEDQ4W
Not being able to see the power wire end, you may need a 12V cigarette adapter. Cut the wire, connect black to black, red to red, ideally soldering them and then using a heat shrink would be best, but cheap butt-connectors and electrical tape will suffice. Here is a 12V cigarette lighter plug on Amazon for $14.00
https://www.amazon.com/dp/B0016LG0CY/ref=cm_sw_r_apa_i_dprFEbRVC4YAQ
Your antenna seems to be incomplete as well. Consider buying a new, magnetic mount antenna. It includes the coax cable and is USUALLY pre-tuned for 11M (CB radio) out of the box. You SHOULD tune all radio/antenna pairs with a SWR meter, which I will discuss/link below, but in any case, here is a magnetic mount antenna on Amazon for $28
https://www.amazon.com/dp/B008ZDBM10/ref=cm_sw_r_apa_i_CtrFEbH7PH3BS
Now that you have your power supply, working radio, and antenna all hooked up, you should confirm proper SWR so that you don't damage your radio. I won't go into all the details about what SWR is or how to go about checking, but here is a link with all of that information for you to look into;
https://www.rightchannelradios.com/blogs/installation-guides/18428275-understanding-swr
Once you've got a grip on that, consider this SWR meter on Amazon for $22
https://www.amazon.com/dp/B002KRME3C/ref=cm_sw_r_apa_i_uzrFEb3DB7KGK
I hope this information helps you. Knowing what you have and what you need can be a daunting experience, especially if you are new to the hobby. This sub is very knowledgeable, as well as countless resources online. You should have little trouble in finding the information you need.
The Uniden 510XL is a fine little rig. While being entry level as far as equipment goes, it's reliable and user friendly, and fits in places you wouldn't believe! As someone who owns 2 of them currently, I highly advise a small external speaker for better audio. They are cheap and can be found anywhere. Here's one on Amazon for $17
https://www.amazon.com/dp/B000ZIC18Q/ref=cm_sw_r_apa_i_IDrFEbRTWHVFQ
As you develop in the hobby, you will learn a lot, not only about the equipment but radio theory as well. It's a very interesting subject, and with all the information and awesome equipment out there, it should provide you with years and years of fun!
Again, hope this all helps. If you have any questions, let me know or drop another post here in r/cbradio
See you on the waves!