Hey Holly,
Congrats on deciding to make the jump! A few things to think about when not using donor bank sperm. Take them or leave them depending on what level of acceptable risk you are comfortable with for your family.
- Infectious disease and genetics screening-
STI's to look for: CMV, HIV, HTLV 1&2, Hepatitis A/B/C (A is common so if his IgM is negative that means he probably had the vaccination), Syphilis, chlamydia, gonorrhoea, trichomonas vaginalis. These are all standard, but do be aware it can sometimes take a few months for some things to show up on screenings, so make sure he's been regularly tested so you aren't getting false negatives.
Genetics Stuff: The big ones are going to be Cystic Fibrosis, Spinal Muscular Atrophy (if caucasian), his blood type and doing a chromosome karotype to see if all those are normal. Other ethnic backgrounds have diseases that are more common in their demographics. I did the Counsyl carrier screening to see what I carried. You may want to think about getting some screening here at least for yourself - if you don't carry anything, then at worst a child would just be a carrier if your donor was a carrier too.
-Check his motives-
A lot of men are altruistic, but like you said there are some sleaze bums who use forums as a method to get free unprotected sex from women TTC. Others might not tell their wives that they are 'donating'. Sometimes they go off the grid and can disappear, leaving you the hopeful parent unable to obtain more samples if you fail to fall pregnant. You also can't be sure if he's sticking to the HFEA guidance of 10 families. Just make sure you are happy with his reasons, and have enough time to get to know his personality. You don't want him to not be there if you get pregnant, and three years down the road want a full sibling and he's out of sight, out of mind.
Sperm Quality
Just because he's achieved pregnancies doesn't mean his sperm is optimal. Men go through sperm cycles - it takes about 3 months for sperm to mature and be able to do their job. You could be catching him in a 'trough' rather than a 'peak'...most frozen samples are going to have more than 20 million total motile cells per mL, as this is where the science shows an observable plateau in fertility rates. Low sperm count is