Wireless?
Even though wireless has come a long way, still many homeowners today don't have secured networks and you need a good router, most people don't have. So that why if you can, go wired. which brings you to the next choice.
Dome is good for out doors, someone once told me, because less bugs will build nest and webs in front of the lens. That answers the question - which one is better, bullet or dome?
Network or no network
The 2 choices you have to make next is if you want to have a Digital Video Recorder(DVR) or a Network Video Recorder(NVR), in the NVR category you have the possibility to use a personal PC and run a program that "works" but, dealing with "windows" "updates" and setting it up so it works, is a pain, just get a NVR
DVR receives a video signal and thats what it records, the downfall is you need to run 2 wires, power and signal, maybe a 3rd if your camera has sound.(sometimes those are combines into 1 wire) but you still need to provide the power for each camera, hopefully your DVR has a power supply.
NVR on the other hand needs only one wire, one CAT5 or CAT6, and most likely your NVR has POE(Power Over Ethernet) meaning the same CAT5 or CAT6 wire will carry power thats being "injected" by the NVR. And the quality of the video is pretty good, just found this on Amazon 4K Camera system.
Network or no network
Now it just comes down to quality of the video, go with at least 720p, anything less, don't even bother. A system like the one at the beginning of the post, is 1080p. and the one just above this is 4k... But what does all that means.
Long story short, those are the number of horizontal lines the video will have. Pretty self explanatory except the 4K which will have, NOT 4000 lines but only 2160p, or lines.
In Conclusion
The greater the lines, the nicer the image, and if you ever have to review a "tape" the more you will be able to distinguish a face and "zoom" into an area.
Network and wired is my personal choice, with a dedicated NVR, not a personal computer converted.
Hope this information was usefull.
Thank you for reading.
-AI
BTW. I have used Foscam, now called Amcrest, great prices, good quality, and they have a nice setup to view the cameras from your phone.