If you are taking a trip to Ecuador you are going to meet a warm and endearing people. Ecuadorians take a lot of care of their visitors. So it's up to you to behave in the same way. In the same way, if you are going to very isolated villages, like in Amazonia for example, then be very respectful of their behaviour.
If you've already had the chance to travel about elsewhere in South America then the comparison will be even easier. You trip to Ecuador will make one thing clear, the Ecuadorians are without doubt the most welcoming, moving, warm and endearing people on the whole continent. When you walk around town or if you use public transport you'll notice that the locals are very curious and always want to talk to you. You'll get lots of invitations for a cup of coffee or a meal with the family. You'll obviously have to watch out for a few dishonest people, but if it feels right, then don't say no. It's also not unusual to find the police or the fire brigade giving you a lift. If you are outgoing you may find yourself drinking hot chocolate at Quito fire station.
As for clothing, you don't need anything special unless you are going to Amazonia. In that case avoid short clothes if you are going to visit villages that are deep in the jungle. In any case, the mosquitoes will remind you if you forget. You should show great respect for the villagers' customs and beliefs. You should also not take their photographs without asking permission.
Generally, keep shtum if anyone talks about politics.
Bargaining when you are at the market is not considered impolite. In fact it's normal. Ecuadorians bargain. So you can do the same, but do it in Spanish and make sure you are smiling.
Although begging isn't a common or major problem in Ecuador you will get children asking for a pen for school, some sweets, or money, shouting "One dollar!". You shouldn't encourage this begging which can only get worse. If you want to give gifts of money, time or material, then talk directly to the charities in the country.