Butchered meat is generally sterile except on its exterior. (That doesn't mean parasite- or botulism-free, but it's a start.)
Get the best quality you can from a source you trust. Keep it at as low a temperature as possible, and don't expose it to warm air for more than the few minutes it takes to prepare.
Cut with a clean knife on a clean surface. Put it right back into the fridge at a very low temp.
Salt and acid, if you use them in your sauce, will provide some anti-bacterial benefits, but this is not foolproof.
People all over the world eat raw meat, but it's best to start with small amounts and see how your system handles it. If you're a child/pregnant/old/sick, it's much less of a good idea.
I think that your problem doesn't come from using the wrong cut, but from using the wrong quality tier of meat.
The cheapest pork in the supermarket, no matter which cut, is produced from cheap mass-held pigs with a certain type of "lifestyle" - no movement opportunities, cheap feed, lots of antibiotica. It produces a certain kind of meat, known as PSE meat, which stands for "pale, soft, exudative". The last word means exactly what you describe: a meat which loses lots of water during cooking. So no, you cannot get more "bang for the buck" by changing the cut.
I still assume that you are getting a better price per gram cooked meat from buying cheap meat and cooking it down than from buying expensive meat which will lose less water, so I guess that, if price is the most important part for you, you shouldn't change anything.
Another word about quality: the S in PSE is also your enemy when making goulash. Generally, you want lots of collagen in goulash, and some fat for taste. PSE meat has almost none of them. The old idea that cheap meat is best for goulash comes from times where the difference in meat prices was based on the cut: a shoulder cost less than a filet, and that was it. Nowadays, this connection still holds for the same animal, but if you look at the different price tiers, the cheapest meat, especially in pork, is not at well suited for long and slow cooking methods. If you buy cheap meat, the best you can do with it is usually mini-steaks or schnitzel, heavily dressed to make up for the lack of taste.
Best Answer
What makes them suitable - You'd want to focus on cuts that are especially lean, without a lot of connective tissue or fat, marbled or otherwise. Raw fat is probably unappealing, flavor-wise, and that's what often causes meat to go rancid, so focusing on cuts with just muscle tissue, and minimal marbling is what makes it good (and safe) for tartare, I'd think.
Cheaper cuts that are good for stews or slow-cooking often have a good bit of connective tissue in them, which would make them poor choices. Unless you like a gristly tatare. :D
Probably round or rump, and sirloin - all already mentioned by you - would be decent choices for those reason. I'm not sure you'd need to look further. Of those, sirloin has the reputation for having more "beefy" flavor, but round and rump are often among the cheapest cuts.
EDIT - UK and USA cuts by the same name are not, apparently, identical cuts. Please see the comments to this answer.