Quoted from Daditude:
The Shadow is an absolutely fantastic game (as the ranks and reviews reflect). If you have a chance to get it, I would 100% recommend it. It is deep, fun, and has tons of shots. It is a very long term keeper for most.
Road show is a love it or hate it game. It has so many mechs and toys, it would cost $15,000 or more if it were made today. It has lots of shots and very funny call outs. It is also priced very cheaply for what it is.
Johnny Mnemonic is another awesome game. Much like The Shadow, it would cost twice as much if it had a theme of a top movie instead.
High Roller Casino is likely the worst of the ones you listed. It is newer than the others, but the shots and the ruleset are just ok. The artwork and sounds get panned...but this is where I say to go for what is important to you. If art and sounds aren't high on your list, no worries. It is also cheap...if you can find one.
Lethal Weapon 3 is a cool game that would be a good starter pin. Cheap, easy to find, fun rules. Some people hate on data east, but I think they have about 5-10 really good games that hold up well. This is one of them.
STTNG is another phenomenal game, but up there in price. If you can come up with the extra money for it, I'm sure you would be glad you did in the long run.
Sharkey's shootout is another game similar to high roller casino in that it is newer, wasn't well received, harder to find, still cheap, and gets panned for artwork and sounds. The ruleset isn't deep, but it is fun. If you have a chance to get one at a good price, it might be the way to go.
The great equalizer is "how much can you get it for?" Any pin becomes far more desirable the cheaper it gets. I will tell you that most everyone would say to get the shadow and sttng, but if you don't have the funds...that doesn't help. Likewise, if you find a working sharkeys shootout for 500 bucks, you need to buy it. NOW!
The other thing I would mention is variety and a deep ruleset. It is of colossal importance in a home collection. Any game can get tiresome if it's the only one you have or if it is too easy. I becomes immediately apparent when they are in a home setting. If I had a 3500 budget...i would ask what 2 pins I could get, and how deep they are for longer term ownership.
It is quite possible you could get a sharkeys shootout and a LW3 or high roller casino for 3500 combined. If you could, I would do that. Otherwise, I would seriously consider combing ads for a low priced sttng or The Shadow. Just my .02 cents.
To add a few more items to consider to the pile, Road Show is a widebody game which turns some people off. The Red and Ted heads are also a PITA maintenance wise, but if they are working well and the game was well maintained it shouldn't be an issue. There are a lot of modes in the game, but they also progress in a linear fashion, which some people don't like. I actually like the game a lot personally and it's on my short list as well.
Shadow is a great game also, but a bit non-traditional in the sense that it doesn't have pop-bumpers and has the upper playfield with all the kickers going on. Again, great game, but if you're looking for a "traditional" pin, it may not be for you.
I own a JM and I think it's a great game, lots of fast shots and there is enough going on in the game to keep it interesting.
HRC and LW3 will likely be the cheaper games, but also much worse games IMO. They will also be the hardest to resell. What games people like is all subjective for sure, but I would not overpay on these games just to score one, because you will end up selling at a loss.
To get back to your original question, you are obviously buying at a weird time with COVID concerns making buying, selling, and moving games into a legitimate health concern. the market is also fairly stable right now and prices don't seem to be dropping like a lot of people thought they would, so there isn't a ton of "inventory" available, so when good titles like the ones you are after come up they tend to go quick, especially DMDs in the 3K range as it seems to be what everyone is after these days. I wouldn't take any "rejection" personally. You know the games you want, which is a great start. Keep an eye on here and if you are on Facebook get into a lot of the pinball buy and sell groups, many have 5-10K members.
In all honestly, a lot of games just change hands among groups of collectors in certain areas too. Of all the games I've sold, only a handful have ended up with someone I met for the first time, and same with games I've bought. The longer you hang around and get to know people the easier it seems to be to come across games. Obviously that's kind of challenging now unfortunately as locations, leagues, and shows have pretty much stalled out. The best advice is to have cash and be ready to go see the game. Don't be afraid to ask questions, but go in person and see the game and ask them there. It lets someone know you're serious. I can't even keep track of the people "very interested" in a game that I've spent hours getting more pictures, describing things, sending emails, etc. only to have them either stop responding completely or pass on the game. Now I just throw up a few pictures and people seriously interested in the game will end up coming to see it anyway.