Let's see ,a 2004 Piston team was built around the paint presence of Ben Wallace.You will need a similar defensive anchor but these type of guys come costly and have great value.
It really depends on what team you're gonna use cause i could suggest a guy like roy hibbert for that role, but if you want realism in your association the pacers would never trade a guy like that.
Other big men that fill the role of paint protector and rebounder are Larry Sanders! (he avgs 12 rebounds and 2.5 blocks in my second season),Andre Drummond (if you choose Detroit) and even Javale McGee or you could go the Celtics way and have a PF as your rim protector with guys like Anthony Davis(that the Pelicans would never want to trade irl) or Josh Smith.
You also need glue guy type SF in the mould of Prince.Prince was mostly known for his length defensively and his mid-post game ,including passing ability.
Three players come to mind that fit that role perfectly.One is Nicolas Batum of the Blazers with terrific length and defense,who also can give you outside shooting and assists in the flow of the offense.
Another Prince like player is Gordon Hayward of the Jazz also a nice 3pt shooter ,passer and of course a lengthy defender(he's got the chasedown block sig skill).He is a bit slow to defend against guys like lebron and paul george(he is out of the question unless you choose the pacers as your team), but he makes up with size.
Lastly you can try Kawhi Leonard, a 3 and D guy meaning that he drains his corner 3's and is a great defender.He is 6.7 ,so shorter than the other two guys but much quicker and a big leaper.
What you can't replicate in the current nba is the mid post game of prince.Guys that are good options from the mid range and the post are Danny Granger,Caron Butler,Carmelo,Paul Pierce etc but are not exactly known as more than average defenders.
For the Rip Hamilton role you need a SG that is really good at coming off screens without the ball and shooting mid range and beyond.So you don't necessarily need a one on one scorer but a sweet shooter ,a bit athletic that is fast to navigate around off ball screens.
The most obvious comparison to Rip is Ben Maclemore the rookie SG of the Kings.Sweet shooting stroke,very athletic and becomes a pretty good defender after season 1.His only problem is his low consistency ,which means that you'll have a hard time shooting over 45% on a game to game basis.
Other guys that their games look similar but not exactly like Rip ,are Klay Thompson(slow though),Caldwell Pope of the Pistons and Oj Mayo (a little bit undersized) that are also ok defenders and won't mess up your rotations.That's why i won't recommend Kevin Martin of the Wolves.His defense is as sucky as it goes.
Finally you need a floor general that won't be a ball dominant or a score first guard.Someone that is a passer,playmaker and a spot up option when the ball is not in their hands like Billups used to be.You also need them to have enough size like Billups ,but sacrificing athleticism in the way.
A guy that looks a lot like Billups is Jarrett Jack of the Cavaliers.Great shooting stroke coming of screens and a good passer too.
Or you could go 6.6 with Greivis Vasquez that is also a playmaker,pnr maestro and has a wet shot from outside(no shoot off the dribble ability though).Be careful with Vasquez on defense ,cause he is slow and gets torched easily by the new era fast guards like Irving,Steph Curry,Derrick Rose etc.
Lastly Calderon,might be old and the definition of matador defense, but he is a great fit for any team with his playmaking ability ,his outside shot and his free throw shooting.
Have fun,the 2004 Pistons team is one of my favorites and every year i start an association that i try to replicate this no-superstar type of team.