Okay, I'm going to go through the sequence here pretty much "in order":
1) Post-prep cleaning.These are old models, and are lead. They may still have mould release (talc) on them, the moulds may have been a bit worn when these were cast, they may have a bit of bloom (lead oxidation), and may even have been painted before.
Assuming they are not already painted, after cleaning off any mouldlines I would recommend giving them a thorough wash in hand-hot water with dish detergent and a toothbrush.
I also suggest buying some cheap toothbrushes for this - the bristles will be stiffer and clean better than using an old brush, and they are pennies each anyway (literally; I think I spend £0.19 on each!).
Then rinse them, and let them air dry on some paper towels.
2) Initial smoothing and sealingWith old lead models, you can gently scrub the bigger areas with a little wire wool or with a strip of some very fine-grit sandpaper at the prep stage prior to washing to help smooth away any roughness.
However, the old lead is often quite soft, and it can be a fine line between improving and worsening the surface of model unless you are willing to spend some time on it.
Instead, if the surfaces are not too bad, you can use a brush-on Polyurethane varnish (get something decent from a DIY store) to coat the main areas and help smooth them.
Doing this after washing the model helps it stick. If you want, you can give these areas more than one coat, but I would be wary of filling details if there are any.
Regardless of whether you spot-varnish any areas to smooth them, applying a very thinned coat to the whole model may not be a bad idea either, as it seals the model fully (always a good idea with lead models, and it helps to protect them from lead-rot too).
3) PrimingUse a primer to coat your models with an initial layer of paint. I used to undercoat by hand, but switched to spray-priming because the results were far better and faster. Specifically, the spray-on primer was more even and adhered to the model better. Unless you live somewhere very dry or very humid, I think you're better off with a spray primer too.
I use an automotive primer than comes in a rattlecan. It is specifically formulated to stick to metal, and to provide a smooth even coat outdoors without being too fussy about moderate ambient conditions.
The one I use is a sandable primer, but also contains a lot of solvent too. This is good as it gives you a smooth application, and lets the filler in it settle into the surface of the model to fill in scuff and scratches and light pitting.
You can get the primer in several colours too, and these can help you depending on what you're painting. Black is good for darker or neutral schemes, and white is good for lighter or brighter schemes. Black has the additional advantage that if you miss any bits, they are dark and won't stand put much on the finished model.
However, I find black makes the model hard to see when painting. My compromise is to use a mid-grey colour primer that gives you the best of both black and white, and is also easy to see. It takes reasonably little effort to bring up any colour from grey, and silver paints sit well on it too.
4) Applying primerIf you are too far from the model, the paint droplets start to dry before they hit the model, and you get fuzziness. If it is very hot/sunny/wet/dry/humid when you spray, this will affect the paint before it hits the model. If you are too close to the model, the force of the propellant can spoil the paint already on the model and you will also get too much paint landing in a small area on the model.
When you apply the spray you need a distance of about 8-10 inches from the nozzle to the model. Start spraying slightly in front of the model, and then move your can past the model fairly quickly to give it a light coating. Keep turning the model and passing it with spray a few times to get it mostly covered.
You don't always need to fully press down on the can's nozzle either, especially when it's fairly full, because too much paint will be deposited on the model in one go.
It takes a little practice, but it's very easy to get the hang of quickly!
After applying the spray, I let the model sit undisturbed for at least a full day. It's touchable and paintable after a couple of hours, but I've found that the paint will keep shrinking onto the model and hardening if you let it, and that it's much tougher and less detail-obscuring if you do.
Finally, if you are using old cans of spray primer, or if they are nearing the end of the can, don't use them on your models - you run a high risk of getting a fuzzy finish. I keep the older cans for undercoating terrain, where the fuzzing may not matter or is even beneficial.
5) PaintingWhen painting, avoid touching the models (I see you have them on corks already - good man!).
When applying your paints, use a white ceramic palette (an old plate or tile works well) to put paint onto and add a little water to thin them down. It takes a few more coats to cover than just using the paint straight, but you get a lovely smooth finish and it makes jobs like highlighting much easier. Plus, it's easier to correct mistakes with a clean wet brush as you go!
Another benefit of a palette is that it lets you put paint onto the brush in a controlled manner; so you don't overload the brush, or pick up any dry bits that may have fallen off the rim into the pot, and you can twirl the brush a little to get a nice point.
6) SealingWhen the paint job is finished, I seal them with varnish before touching them - this stops my greasy fingers from spoiling the delicate acrylic model paints!
I start with a non-yellowing UV-resistant brush-on varnish (DIY store again, or use the same stuff for step (2) as for this step).
Then, after a day's drying, I use a spray-on matte varnish that kills the shine (Testor's Dullcote).
Sealing has the further benefit of smoothing the final finish some more, adding protection to the model (helping it resist chips and scuffs), and still provides a nice end result.
I also find that the sealing stage helps to make the colours look more saturated.
Phew, a long wall of text! To be fair, most of the above is actually very fast (and you're likely doing much of it anyway) - it may seem complicated only because of all the explaining.
You can of course do a lot more, but trying to achieve a clean smooth surface before you prime, when you prime, when you paint, and after you paint is all very straightforward and will improve painting results regardless of anyone's skill.
A very good case for this was made by Seb Archer in the tutorial
here. It showed me that the difference good prep work makes to a model is huge! So much so that it's never a stage I skip on any more, as even a simple painting effort can be made to look much superior.
Anyway, I hope that my comments here help you in your next batch. For the models you have already done, you can strip and do them again if you want, or you can try a couple of thick coats of gloss varnish and a dusting with matte spray if you want to "fix" the fizziness a bit.