I prefer the separate cable modem option, because it gives you many more choices as far as the WiFi router goes. Also you can keep the old cable modem and just upgrade the wireless router as technology advances. I have had several different wireless routers connected to my Motorola SB6120 DOCSIS 3.0 cable modem over the last 4 years.
As far as the router goes, I personally use a Netgear Dual Band WNDR3700. http://isp1.us/reviews/netgear-rangemax-wndr3700/
Wireless signals are affected by many factors including distance, wall density, electrical interference, directional antenna range, etc.
All of these factors will affect your actual wireless range. As wireless connection quality varies the connection speeds are renegotiated. The WLAN connection may start at 150 Mbps and end up at less than 20 Mbps or drop entirely.
I have a ISP site and blog, a couple of popular high power routers that my visitors have recommended are,
ASUS RT-N66U Dual-Band Wireless-N900 Gigabit Router - http://www.amazon.com/gp/product/B006QB1RPY/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B006QB1RPY&linkCode=as2&tag=excharge-20
The Amped Line which includes Wireless routers, wireless extenders, and wireless access points. http://www.amazon.com/s/?_encoding=UTF8&camp=1789&creative=390957&field-brandtextbin=Amped%20Wireless&linkCode=ur2&node=172282&tag=excharge-20
However, Just because a particular wireless router works good at one location does not guarantee that it will have similar performance in a different location due to variance in the factors listed above.
You should try to centrally locate your wireless router or gateway up high and away from dense walls and electrical and 2.4 GHz wireless interference such as microwave ovens, cordless phones, baby monitors, etc.
For poor WiFi connections, you could try adjusting the position of the router or relocating your device closer to the wireless router to obtain a stronger signal.
If you still have a weak wireless signal you can either get a wireless extender or a new wireless adapter with better range for your WiFi device.
Devices such as wireless extenders can expand your wireless range. The wireless range extender receives weak wireless signals and repeats them to extend the signal range to greater distances. Some models include Ethernet port(s) in addition to the wireless radio.
Here are the two most popular highly rated models on Amazon.
Securifi Almond - http://www.amazon.com/gp/product/B0087NZ31S/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B0087NZ31S&linkCode=as2&tag=excharge-20
Netgear Universal WN3000RP - http://www.amazon.com/gp/product/B004YAYM06/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B004YAYM06&linkCode=as2&tag=excharge-20
Your best bet, especially for serious online gaming or streaming, is a direct Ethernet connection between your device and the wireless router. Ethernet is very secure and unaffected by wireless interference and will give you a rock solid, stable network connection.
If it is not feasible to run Ethernet cable your next best option is to use powerline network adapters. I wrote a review here: http://isp1.us/reviews/netgear-xavb2101-powerline-adapter/
You plug one in by your router and one in the room where you need access and connect them to the devices with standard Ethernet patch cables. The network signals are transmitted over your existing home electrical wiring which will not be affected by wireless interference.
Cisco/Linksys is a decent manufacturer, However no matter what you decide to buy, as far as the brand goes, the brand is not as important as the model. Some manufacturers release a good model but the next is crap. I would look at the Amazon reviews of models that interest you. Even if you don't buy from Amazon the reviews will tell you a lot about which models to avoid. Look for at least 15 or more reviews with a 4 star or better rating. Read a few and see if they sound like the particular model will work for your application.
Good Luck...