It is a bit difficult to answer because rosters vary so much from one person to the next. Obviously peak season summer rosters are busy and subject to change. Some people will have leave and requested days off which will make the rosters of those who don't even busier. However broadly speaking if you are a 757 only pilot ( some are mixed fleet 757/767 ) at LGW you can expect a summer season that might typically involve flight cycles that rotate through a full 24 hour spectrum. Night flights will involve round trips to Spain, Greece and Turkey. Long round trips to Egypt are (FTL restrictions) normally day flights, but you can expect these to be on a roster as well. Day flights will include scheduled service flights to Spain/Canaries and Portugal as well as charter flights to Spain, Italy, Canaries, Greek islands, Cyprus and Egypt.
You can expect 8 to 10 days off typically in pairs with occaisional single days and the odd (very odd) 3 day run of days off.
There will be some flying from other bases and that might include nightstops at those bases, but the majority of flying for LGW based pilots will be as described above.
In winter there tends to be more days off and many more standbys. There is also more ad-hoc flying ( football charters etc.) that may or may not involve nightstops. The scheduled flying continues, however the charter flights tend to be to the further (sunnier) destinations. Expect longer sectors with the flights to Egypt, Gambia, Canaries etc. After mid December, weekend ski flights will also figure in the programme.
There is some "jam" in the 757 winter programme, that varies from year to year. This might include some overseas contracts, a few long haul charters, and even 3 week plus "Around the world flights". However this type of flying is not sufficiently common to figure significantly in most programmes. Nevertheless it is there from time to time and does add a bit of variety to some winter programmes.
For Standby, you have to reside at a contactable address that is within a maximum 90 minutes travelling time of your assigned base. You will be called out on a significant number of occaisions and you will also be subject to a significant number of standby conversions into duties prior to the date concerned. Standbys aside you will also ( particularly in the summer ) be subject to changes to your planned roster that mean that the programme you do may be very different to the one that was planned when the roster was produced.
Take home pay obviously depends on your own tax situation and I will leave it to someone better qualified to answer what might be typical in the situation you describe. Flight allowances again vary from person to person, but at LGW on the 757 you are probably looking at around £ 4000 PA, with some variations.