Hello jztilly, and welcome to CS. There are people here who are much better qualified to answer these questions, but since none have responded yet, here's my two cents worth.
One of my machines, which I did most of my learning on, is a Gaggia Classic, not too much different from a Via Venezia. It came with a panarello, and one of the best things I did was to replace it. They are supposed to make it easy for beginners to froth the milk - and they do that. But we don't want just froth and bubbles on top of the milk, we want well textured milk and micro-foam, and for that you need a plain wand with a simple tip.
Pressurised portafilters are made to cover up problems with stale supermarket beans, cheap and nasty grinders, or people who can't or won't bother to learn how to pull good shots without them. But they only hide the symptoms, they don't fix the problems, so the coffee is still crap. Because they hide issues with beans, grinds, and technique, you will not learn or improve much while using one.
Before getting into extraction, I suggest that if you have both a single and a double basket, you should put the single in the back of a drawer, and leave it there, at least until you have mastered the double. If you don't have a double basket - get one.
Extraction depends on a many factors, but with a no-frills machine like the Via Venezia, there are four main ones you can control. The first is good, freshly ground beans, then there is dose, grind, and tamp. The last three must be considered together. When I first started my coffee learning curve, it took me a while to fully grasp this.
The dose (depth) of coffee in the basket will affect the extraction time/flow as much as the grind. A few grams more in the basket will reduce the flow and have the same effect as a finer grind. A few grams less will have the same effect as a coarser grind. So if you increase or decrease the dose, you have to grind a little finer or coarser to compensate. When you get the dose/grind combination right, you still need to tamp well, but it becomes less critical. For consistent results, you need to be able to measure your dose accurately - near enough is not good enough. Filling the basket, leveling and tamping can work, if you use the exact same routine each time. Then you need to find the right grind to match that dose.
A good extraction is usually defined as 50 to 60 mils of espresso delivered in 25 to 30 seconds, with the shot stopped just before it starts to blonde (turn pale). I can only achieve this with a triple basket and 17 - 18 grams of beans. With a double basket and 14 - 16 grams I only get about 45 to 50 mils before it pales, usually nearer to 25 seconds than 30. A finer grind will slow it down a bit, but doesn't increase the volume before it starts to look pale & weak. Maybe I'm still missing something here, but I like the coffee I'm making, so it doesn't bother me.
As you have mentioned, you should get a better tamper. For starters, it doesn't need to be expensive or super flash looking, but it does need to fit neatly it in the basket.
Hope this helps - deegee.