Greetings,
Dee
Given that you've already gone through the gamut and reduced your choices to Gamo or BSA, I'll forego the usual list of preferred makes and models. I don't own a break barrel BSA, let alone a Lightning XL SE - GRT. So, I can only speak to the quality and accuracy of BSA in general - which is very good! The BSA line are famous in the Field Target and Hunter Field Target game. Let that speak for itself.
I have owned several Gamo break barrels. As you've already noted, the Gamo line is less expensive and this is a reflection of overall build quality. Inside of 35 yards they are accurate enough to do a bit of pesting. But, I wouldn't take them to any competitions.
The one caveat I'd mention regarding Gamo is that I had some trouble with their 10x Gen2 design and would recommend a Gen1 rifle instead. They have started releasing the Gen3 models and I'm waiting for the Bone Collector to become available so that I can try it.
As for your question of caliber, definitely .22 will serve you better versus "feather and fur prey".
~ Mondo