Firstly do you (or parents) have a specific budget? This will really determine what you can get, as much as what you should get. I'd suggest joing
www.stirton.com, this is a British smallbore forum; rifles are often offered for sale, and advice can be sought.
If your budget allows a new rifle would be ideal. An Anschutz 1913, FWB 2700, or Walther KK300 would be a great choice. All are mechanically simillar, ahve great triggers, and good stocks. If I was looking to replace my 1813/Gemini, a KK300 would be high up the list. However each rifle will fit and balance slightly differently. Before spending roughly £2,500 I'd want to try each for size.
An alternative would be a Bleiker or G&E. These are Swiss made rifles, more expensive than the German Anschutz, FWB, and Walther, but are both a more advanced design. Both have a very short bolt, so they are easier to load. Both have a superb trigger. Both have superb US-made barrel. But, the cost for the barrel/action/trigger (no stock or sights) is more than a complete new Anschutz/FWB/Walther.
Yes a System Gemini stock is an excellent choice for smallbore. I use the older Ultra model (with the wooden butt section), and find it very comfortable. You can have a Gemini stock for most of the major smallbore rifles: Anschutz, Walther, Bleiker, but not FWB.
I think you may be a little confused, The System Gemini is just a stock, not a complete rifle. Your fullbore rifle may have been built by HPS, but they only made the stock. The action, barrel, trigger, and sights were bought in, and assembled (very carefully, and with great skill) by HPS.
If your budget is limited, and it is for most first time buyers, look at a second hand rifle. .22 barrels last a long time, so a used rifle can still be very accurate. I'd look for the newest and least used barrel/action you can find. If the stock isn't perfect, these can often be made to fit with a little woodwork, or replaced with a newer one at a later date. Roughly speaking £500 would get you a wood-stocked Supermatch rifle from the '80s or '90s; this means Anschutz 1813 or 1913, Walther GX-1, or FWb 2600.
Most of the rifles I've mentioned about are the heavier free rifles. You say you are of slim build, so you need to make sure the rifle is comfortable for you, sometimes a lighter barrel can be more comfortable.
Tim