Having been cathed in hospital about a half-dozen times, and self-cathed maybe twice as often, I've some definite thoughts:
My first experience was having a Fr 16 latex Foley inserted by a nurse for not being able to pee after surgery under general anesthetic. This Post Operative Urinary Retention (POUR) is apparently quite common in both men and women. She emptied the lube packet int the sterile tray and dipped the catheter into it. The insertion was fairly slow and a bit ouchie, but the relief was wonderful. There was soon over 1000ml of pee in the bag! After the cath removal a day later, peeing was very ouchie, although the feelings went away with succeeding pees. In retrospect, the Fr 16 was a bit too big for me.
The subsequent insertions in hospital in the following several years were all pretty much the same, except I insisted they use Fr 14 size. This had a down side , since Fr 14s were not stocked on the floor, I had to wait with a painfully full bladder until one was gotten from central supply. All the hospital caths were either red rubber straight caths or silicone coated latex ones.
The first few times I tried self-cathing I used Bard kits, bought new. I never knew about injecting sterile lube into the urethra until someone mentioned it here, and I then went looking for cath kits with the appropriate lube applicators. Some cath kits come with pre-filled lube syringes, but it is unclear if they are designed for insertion. I've only found a single brand of catheter kit with a lube applicator clearly designed for injection.
I have never had an anesthetic lube injected, and would not, because, as I've written before, pain is the body's way of saying STOP. Unless you're an expert professional at this, I'd strongly suggest never using an anesthetic gel. I do agree, it's a pity that syringes or applicators, pre-filled with sterile lube, don't seem to be available in the US in reasonable quantities.
As to fast or slow insertion, I'd always go with slow for reasons of caution. Going slow likely is a bit more ouchie, but it limits damage should something go wrong. If a cath is being inserted into you by a nurse, she cannot know she's hurting you and it takes some time for you to say 'stop' and fer her to process that. Consider, would you rather run into a door or walk into one?
When the cath tip gets to your prostate, don't just push it through. Try to relax, as if you're peeing, and it may slip through more easily. Also, unless you're having a residual pee test, cathing with a part full bladder is easier because you can see by the pee flow when the cath is in you far enough to inflate thye balloon if you're inserting a Foley. You don't want to insert with a very full bladder either, unless needed. When it's very full, the muscles are trying to hold your urethra closed hence making a cath passage harder. I usually insert with a few hundred ml of pee inside... ie: not having peed for a few hours.
Finally, before you cath for play, be well aware that it can cause a UTI, either because of poor technique during insertion or just because you have a cath in. The longer a cath stays in, the higher the probability you'll get a UTI. A quick in, pee, and out with a straight cath is unlikely to to cause an infection. Put a Foley in for a week and your chances are maybe 20%; and if it's in longer, getting a UTI is pretty much certain. And you really don't want a UTI. Getting one often means a course of antibiotics. And antibiotics not only kill the bad microcritters in your urethra but also the microcritters in your bowel that process poo.. Even if you take a probiotic, it's quite likely that you'll get the runs... badly enough that you'll NEED diapers.
In summary:
Be careful, cathing takes sterile technique.
Go slowly and never force anyting.
Be aware that cath play can cause real life problems