I want to haul cargo freight in a Mini-Cooper. But ...realistically... that is not going to work.
You Expectation have to be realistic relative to the speakers you have. I think the RS1 are 5" (130mm) at best. That only moves just so much air, and only goes just so deep. That's the nature of the beast.
Actually it is a 150mm 6" bass driver according to this review -
Monitor Audio Silver RS1 specs
Most Subs have one of two connections -
Line Level (pre-out, sub-out) or
Speaker/High Level, the second of which connect directly to the amps speaker wires. Many Subs have Both of these.
Given that the speakers go down to 43hz at -3db, it would probably work best if you either get a Subwoofer that can be set to 40hz or below, or that you add some Bass Management to the Front Speakers. Though you would set the Sub in the 40hz to 45hz range.
Generally you either have some degree of bass management or you set the Sub Crossover at the natural Roll-Off of the Front Speaker, which in this case would be in the range of ~40hz.
To add Bass Management, very limited Bass Management, you could use RCA "Y" Splitter cables attached to the Pre-Out and run one leg to the Sub and the other leg to the Power Amp.
In the Lines going to the Power amp, you could potentially add
High Pass Filters similar to these to limit low frequencies in the Front Speakers.
"Harrison Labs FMOD Inline Crossover Pair 50 Hz High Pass RCA" from www.parts-express.com!
"Harrison Labs FMOD Inline Crossover Pair 70 Hz High Pass RCA" from www.parts-express.com!
"Harrison Labs FMOD Inline Crossover Pair 100 Hz High Pass RCA" from www.parts-express.com!
Likely 70hz High Pass is the best choice. Unfortunately these are USA links, I don't have EU/UK links to similar products, but most likely they do exist in the EU/UK.
With these in place, you can set the Subwoofer Crossover to the matching frequency. As suggested 70hz, though 50hz and 100hz are also available.
If you are going to simply blend the Front and Sub, then you can use the speaker terminals and simply set the Sub Crossover to match the natural roll-off of the Front Speaker (~40hz). In this case the Front speaker will still be running full range, but the Sub will fill in the very lowest end of the frequency range.
Connecting the Sub to the speaker terminals will not add any load to the amp, it won't even know the Sub is there.
As to Subwoofer, though there are alternatives,
BK Electronic makes good Subs at a very fair price. With your budget, the
BK Gemini-II 10" is probably the best choice -
Sub Woofers - Sub Bass - Subwoofer
Gemini
Just a few thoughts.
Steve/bluewizard