Hi Med.
Your budget will kind of define what you will buy.
Buying second hand can often be a good shout....you could pick up a more expensive better-built rifle for the price you might pay for a cheaper new one
Accuracy is more important than power......too much power can work against you with a spring rifle.....far better to have a smooth shot than have the rifle jumping all over the place.
Not to mention the effects of overpowering will have on the ballistics side of things.
There is no reason that you could not shoot out to 45yds with either a PCP or a Springer.........as long as you have a good understanding of the basic Marksmanship principles.
Practice....practice....practice is the way to go.........again....a half decent rifle will help.
The hold of a springer is important to master to get the best from your shot.....look up Artillery hold.
The fit and feel of a new rifle is important........Determine what length you are happy with.....the weight.........and of course what calibre you prefer.........scoped, or open sights..........having a scoped rifle is a bonus once you zero and map it out and WILL give better accuracy at the longer distances...... operation of the rifle.....would you prefer break barrel......side lever.........underlever cocking action.
In your OP you said you wanted to take small game on occasions..........goes without saying that you need to master the targets and rifle before you go for that.
Being a relatively new shooter you could do worse than visit your local RFD and see what is available either second hand or new that is within your budget.
A great opportunity to hold and shoulder a potential choice of the rifle.
Some dealers offer a package deal....rifle + Scope +bag + pellets to get you started.
Keep the very first targets you shoot........pin them up somewhere and watch as your skill levels improve as you move on through the practice sessions.
Having insurance and good knowledge of safe shooting and handling is worth looking into.
