Fully furnished includes furniture and appliances (whiteware) usually washing machine, dryer, fridge and maybe dishwasher. Partially furnished includes appliances only. Serviced Apartments
have everything you need including dishes, towels, sheets etc and are serviced daily.
All accommodation in Singapore is expensive and for 6 months you probably need to look at Serviced Apartment
s as most leases are for 2 years. Try further from the city for cheaper serviced apartments such as Redwood and I know there is some in Butik Timah which are reasonable. They are negotiable for longer terms although are tough to find without booking well in advance.
Or find an apartment/townhouse and buy everything cheaply from IKEA or similar. For the amount you spend monthly on a serviced apartment you could furnish a pproperty easily.
As for balcony and green space, space is at a premium in Singapore and are luxury items. You will find it but you will also pay for it.
We spent a couple of months in various accommodation whilst trying to secure a property
here so have researched thoroughly. Set your budget, with some flexibility and talk to agents, check out papers, websites regularly. Some people travel and rent out their space for short periods but these usually rent quickly as they are sort after and are though word of mouth.