That is not really worthwhile. The proportion of fixed costs is too high for such a small system. Installation, electrician, scaffolding, inverter – these costs are incurred anyway, and even if the inverter becomes a bit cheaper and the installation perhaps goes faster, the difference will not decrease proportionally to the system size. 2 kWp might be about 1.5 kW output at peak times. That is enough for own consumption but only in summer and only if you can use the appliances at noon and cook at noon – but not at the same time, because at 1500 W minus the base load in the house you are already over the limit with stove OR washing machine and have to buy electricity. From autumn until spring, it hardly covers the base load.
With a realistic 30% self-consumption and an optimistic 1000 kWh/kWp per year, that would be about 600 kWh saved. You save about 150 euros per year with the energy provider – please do the math yourself.
This does not mean that photovoltaics are not worthwhile. I have a system myself and after one year of operation and first bills, I can make some reliable statements about whether it pays off. Yes, it does if the system is as large as possible (but under 10 kWp; otherwise, unfavorable conditions apply) so that you still have enough reserves to convert as much as possible to electricity. Because feeding in is no longer worthwhile, but self-consumption more so. Increasing it is an art form and takes a while, but you can increase self-consumption with targeted measures without relying on storage systems, which unfortunately still do not pay off at all, not even approximately.
For example, we acquired an electric vehicle (Twizy), a split air conditioning system (heating during transitional seasons and cooling in summer), a domestic hot water heat pump instead of an instantaneous water heater is planned (next year), as well as app-controlled wireless sockets for perfect utilization of surplus production.
In the first year from Nov 13 to Nov 14 we took 1890 kWh from the energy provider; before that period it was still 3500. Still, of the 7367 kWh produced (7.28 kWp system), we only consumed about 1200 ourselves. That means we also used less electricity. Well, the Twizy and the air conditioner only came in October 14.
Accordingly, I would advise choosing the system as large as possible to have reserves for self-consumption and to make an energy consumption above the base load possible at all, and for as long as possible during the year (Nov/Dec/Jan still look very dark in this respect, because almost nothing comes in then). Better to take stronger modules if space is tight. Better to banish solar thermal to the facade, where it makes more sense anyway, instead of giving up roof space. Also mandatory: Inform yourself further here in the forum (technology! tax issues!!) and get many quotes – the guideline for prices is 1300-1400 euros per kWp – so with your system size, no 3000 euros! Possibly a bit more due to the higher proportion of fixed costs. But as said – better build somewhat larger, i.e. at least 4-5 kWp.