Benefit of fairings
Full fairings do reduce the cold of wind-blast or the amount you get wet but not all fairings are equal. The sportier the bike the more ineffective they tend to be... (The fairing on sports bikes is designed to provide a slippery shape when you tuck behind it rather than sitting normally)
When I had a Deauville (big fairing) I traveled 40 miles into a garage where I picked up a cbf600 (un-faired) as a courtesy bike and rode it for a further 10 miles. I was freezing after the 10 miles but hadn't noticed the 40 miles... (The temperature would be about 4.5 and I was wearing a jumper plus Goretex textile with liners).
Similarly the 250R Ninja fairing was pretty useless at keeping you warm but the bike was still much warmer than a (unfaired) Moto Guzzi Brava that I test rode at about 4.5 degrees. I loved the Guzzi but have never had an unfaired bike and would be reluctant to go that way unless I only used it for short trips....
As to which bike under 500cc I would avoid making arbitrary decisions based on capacity - there really is no correlation between insurance and capacity and barely any correlation between economy and capacity... (My 800 is the most economic bike I have had - more economic than my old 250 and my 700 and my 650 and is one of the cheapest to insure)
If you have to go cheap a Yamaha Thundercat (600cc) might be tempting. Think they stopped at 2003 and I wouldn't expect any to be worth over 2000. Unlike many later 600s the fairing is a little bigger and the bike more general purpose than the things that followed it. There are a lot of other bikes with fairings that would be very good and slightly more general purpose - CB600F even high mileage ER6F should be available below 2000. SV650S is a bit more sporting as is the CBR600F.
Get yourself some quotes and look at all your costs...