That's quite a low budget unless you consider second hand, in which case be wary of how often a second hand tent has been used as polyester tents naturally degrade on exposure to sunlight. Some say the typical lifespan of a polyester tent is 12 to 16 weeks cumulative use but obviously the stronger the sun the less time it will last. You can pick up some bargains that have hardly been used though.
A good rule of thumb regarding size is to go for two berths more than the number of people using it, so for a family of three I would recommend looking at a minimum 5 berth, we have a 6 berth just for the three of us as we like the space.
What do you mean by "patio", just living area or a separate awning?
The Vango Icarus 500 gets good reviews, its a 5 berth so would be ideal for 3 and has a reasonable living area. You would need to stretch your budget though as normally its £189 in Go Outdoors but they currently have an offer on where if you spend over £50 you get an extra 15% off meaning you would pick it up for about £160.
Have you factored in sleeping bags/beds/table/chairs/stove etc? No problem picking these up second hand, but they need to be factored into your needs.
------------- May 2015 - Arrow Bank 4 nights
July 2015 - Manorafon 4 nights
August 2015 - Piccadilly Caravan park 3 nights
August 2015 - Wheal Rodney 11 nights
Sorry Nick, just double checked the Go Outdoors website and the additional 15% off doesn't apply to their "wow" deals, unfortunately the Icarus is a wow deal so the cost is £189. My mistake!
------------- May 2015 - Arrow Bank 4 nights
July 2015 - Manorafon 4 nights
August 2015 - Piccadilly Caravan park 3 nights
August 2015 - Wheal Rodney 11 nights
If you are happy to review your budget (unrealistic really for a 4 person tent really) then I would recommend looking at the Vango Icarus 5 person or 6 person as an ideal starter tent. It's easy to pitch as all the poles are the same length and it's got a darker inner tent to help you sleep on a bit in the morning, mesh on the door to help keep it cooler but not letting the bugs in and a host of other good features.
Don't forget to leave a review of all tents you've used, for a chance to win fantastic prizes
A lesser known brand but it gets good reviews on their website and on the reviews section of this website (here). 3000mm HH and it comes with a 2 year guarantee against manufacturing defects.
------------- April 2015 - Castle Camping, Staffordshire
June 2015 - Castle Camping, Staffordshire
July 2015 - Pillars of Hercules, Fife
August 2015 - Fforest Fields, Powys