To buy a home as a primary residence in another area (outside of your commuting area) and use emloyment income, then you'll either need a relocation letter from your current employer to a new location of theirs (which would allow you to purchase a home in the area you are being transferred to), your employer to confirm you can work remotely/from home (which would allow you to purchase anywhere), or obtain a new job in the area you want to move to (and oftentimes will need to begin the job prior to closing on the mortgage). Self-employed individuals would need to write a letter of explanation on how they'll be able to maintain current profits after moving to the new area.
Qualifying with rental income alone wouldn't be probable, as you can only use 75% of it to qualify. So if you are buying a duplex for $200k, payment is $1,500/mo, and the other unit you aren't going to live in rents for $2,000/mo ($1,500 is 75% of it), your DTI is 100%.
Part-time employment typically requires 2 years before it can be used to qualify. With moving to a new area and with brand new employers, it's unlikely less than 2 years would be acceptable.
A family member willing to co-sign could help out with income though.
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