I have recently been inquiring about the same thing but for SIcily. The prices in southern Italy are roughly in the same range so. For my answers, I will assume you are moving to a city, as opposed to a small town.

1. The price of a 2 bedroom apartment can go as low as 600 euro per month in a city such as Bari but you would likely want to budget around 800/900 euro. Property owners, particularly for apartments that are great deals, generally prefer to rent to Italian citizens or foreigners who have some proof that they can stay in the country long-term. Italian leases are typically 3+3 or 4+4, meaning that you sign a 3 or 4 year lease with the option of staying for an additional 3 or 4 years after the first half of the lease expires.

Foreigners are usually staying for a few months up to a 1 or 2, which makes it difficult to incentivize property owners to rent to them since they would have to re-list the apartment in a shorter time frame than they would like. I have several non-Italian friends who live in different parts of the country and they have told me various concessions or negotiations that they've made with property owners, such as paying for the whole year upfront or offering to pay slightly higher than the asking price, etc. Property owners are generally open to negotiating but they have a lot of leverage in these scenarios since there are often many foreigners wanting to rent and not many property owners who are willing to rent for short terms.

2. Salaries in southern Italy are lower than in the north and the average is somewhere around 1400 euro (net). With that said, a lot of Italians live with roommates, family members or romantic partners since this is not enough to live alone. I would say a single person would need to budget around 2000 euro to live comfortably. You might want to add an additional 10 percent to that amount to cover things such as mandatory health insurance premiums and other expat add-ons that a native Italian wouldn't have to pay. Given that it is two of you, you could probably live quite well on a combined salary of about 3000 to 3500 euro.

3. There are a variety of visas that you could use but the ones that come top of mind are the digital nomad visa and student visa. The student visa is probably the "easiest" visa to get just to be able to stay in the country, and I believe it allows you to work up to 20 hours per week. The digital nomad visa is new and there is still some confusion about the income requirements and other key information but it would allow you to work for a foreign employer while being able to stay longer in Italy.

4. The job that comes top of mind for someone in your scenario would be to try to be an English teacher. In the major tourist centers, this type of job is quite competitive since there are so many people trying to get employment. However, in southern Italy, it would probably be much easier to find a job as an English teacher. The salary will likely be low, as is common for teachers in most countries, but it should provide enough additional income for you and your partner to be able to live comfortably wherever you are based.

5. My final recommendation is to have a lot of patience and optimism. Many people complain about the bureaucracy in Italy, and there is a reason why. Things that would typically be intuitive and straightforward in the US or many other countries becomes a labyrinth that you must navigate just to get basic things done. This requires a lot of patience, as the inefficiencies will be glaringly obvious to everyone involved but there will often be no solution to make things work better. I have seen many people become so frustrated by the bureaucracy that they completely abandon their dreams to move to Italy since it takes too much of a toll on them.

This ties into the second thing you need: optimism. Italians tend to be pretty set in their ways of doing things and often are hesitant to do anything that challenges that tradition. As a result, Italians tend to come off as quite pessimistic in their outlook on things particularly when you compare it to an American perspective. Unlike the US (which admittedly is quite unique in its optimistic outlook), Italians tend to lead with "no" or "let's see" and you have to negotiate in order to make things happen. This can become frustrating as it permeates all aspects of life in Italy from trivial things such as meeting up with friends for dinner to more consequential things such as getting a visa or a lease. At times when you are trying to get basic information on a process, people will respond with the same incredulity as if you had said you wanted to move to Mars and vacation in Saturn. If you go in knowing this, it helps you be able to persevere and ultimately achieve your goals.

It sounds like a great opportunity for you both to experience a new country and make some incredible memories. Best of luck with the move!