You can spend thousands and still miss a barn door or spend just enough and enjoy yourself. If you haven't got the talent to start with a million pound won't fix it. Whippet, Russell, a few bang sticks and a flat cap. http://www.smart-tech1st.co.uk
I did try to handle a Walther LGV but the shop only had a LGU in stock which I handed back fairly quickly as it didn't fit me at all and felt a couple of pounds lighter than a Bren gun I fired in the 70s.
Still,I would consider a break barrel but the Air Arms underlevers seem likely to be my choice.
Personally I love all the mentioned rifles, but to be honest I would recommend a Weihrauch HW95K. In .22 they are a joy to shoot, the rifle is not to heavy and being a break barrel easy to load but also very easy to cock. It is a great all round rifle suitable for target, pinking, and HFT.
Shooting Air Rifles is like being a pubic hair on a toilet seat.
Eventually someone comes a long and P's you off.
They usually have a PCP
both the TX and Pro sport are very capable rifles.
The only thing I'd add to the above comments are the fact that both rifles have a different balance. The TX is more nose heavy. This suits some but not others.
If you do plan to shoot targets at further ranges in the future or if you think you may wish to try to try FT / HFT I reckon .177 would be a better bet calibre wise.
Either calibre will dispatch any legal quarry with ease.
Both will be fiddly to load in .177. The breech loading cut out on both makes access a little tricky. The port on the HW97 is more accessible but the two you mentioned are a better "out of the box" rifle.
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