Okay, from my own experience since starting several years ago.
The short version:
There is a risk. There is always a risk.
Do your research before choosing who to see.
You're responsible for your own health and can only trust yourself. Nobody else.
Get to know your own body.
Get tested regularily.
The long version:
There's always a risk, accept it or accept that the paranoia is going to drive you mad and ruin the whole experience for you. It's kind of a balancing act between being concious and aware of the risks and not letting your awareness of those risks and their consequences overshadow the experience and enjoyment of the punt.
On the plus side, I've found that if you're careful and pick the girls you see then many, if not most, of the girls will be just as cautious and conciencious of their health as you are, if not more so. You'll learn to pick up the signs from a girl's attitude towards you and the punt, from her awareness and manner towards cleanliness (her own and the venue) and taking the lead on things like the rubber and keeping the room and towels clean. from that you'll just start picking up the red flags and you need to pay attention to those, it's easy to dismiss them when you're full of juice and gagging for it but in all aspects of this hobby you need to be concious of when your mind or your gut is trying to tell you something isn't right.
How do you pick them? reviews, feedback from other punters, how well they come across in their profile (if they have one). This site is a life saver - research and when reading reviews look for comments on the girl's manner and cleanliness. New girls are a risk. Girls who have been around a long time but have no feedback are an even bigger risk.
Regarding feedback from punters - Beware of fluffies! a review from a fluffy or an overly fluffy review is worthless and probably misleading. These guys are either so overly caught up in having had a good punt, startstruck by the momentary affection from a beautiful woman, or are so intent on trying to score points with the escort that they will unintentionally or even intentionally overlook bad signs including signs of bad hygiene and even symptoms of STI's. Usually it's not malicious, they just don't want to upset the escort or want to "big her up" so she sees how much they like her.
Other punters can be the most valuable source of info on who to go to and if you're looking to stack the odds in your favour it's their comments, feedback and most importantly warnings that you need to look for. I'd be lying if I said this site and it's members hadn't spared me from many a bad punt and probably played a big part in my not having caught anything in all these years. However, take everything with a grain of salt - over time I've learned that many who will often condemn unsafe practices will themselves engage in bareback with regs or girls who are "retired" and are thus not in public view. Be aware that some punters and even some very reputable girls do this and don't let yourself be lulled into complacency or thinking one particular girl is "different". The risk is always there.
Regarding what the escort says - don't trust it. As I said, many girls have their heads on straight, are clean, safe and conciencious of their health and do whatever they can to minimize the risks, but not all and as mentioned above you never really know what the girl is really getting upto. It's not in the girl's interest to admit to having an STI and some depend on the money they make to get by, many more value the money and lifestyle it affords far too much just to drop it. Unfortunately escorts are the among the best, most proficient and believeable liars around - in many ways it's a key part of their job. Doesn't matter how nice they are or how honest they seem, you don't know them and you don't know what they're getting up to with guys in their personal life or "special" clients.
Regarding you - Get to know your own body, particularily your privates. Really pay attention to how they look - blemishes, veins, lumps, bumps, colouration etc while you know you're healthy and clean. Make a note of this, be it mental or written so that if the paranoia or suspicion sets in you don't go questioning whether something looks normal or if it was there before. Been there, done that and believe me your mind can exaggerate anything you're not absolutely certain about.
Get checked regularily. Suspicions or no, make a habit of getting checked at least every 3 months. It's really not as embarrassing as you imagine it will be, the staff don't care and it gives you piece of mind. It also means you're not gambling with health of the girls you see and that of the guys they see - you'd want everyone else to be safe too right?
If you think you've got something - Stop punting, stop any sexual contact in your personal life and get checked. Being open and honest with the nurse will give you the best chance of finding out if you have anything and getting treatment. You'll get a response in 5 days after testing if they pick up anything. HIV is VERY rare and VERY unlikely with protected sex but you'll need to get tested 3 and 6 months after in order for them to detect that. There's nothing you can do while waiting for results so don't go driving yourself up the wall researching every STI and concluding you may have it, just occupy yourself with something else and remember - no sexual encounters until you get the results.
I've never had an STI from punting. Some of that is luck, most of it is being careful and minimising the risk.