I went into this issue in great detail due to peculiar aspects of the effects I wanted IMTU.
To recap- I have instantaneous jump but the travellers experience 1 week on board.
That's because I couldn't stomach jump space anymore, but wanted the staterooms and economics of passenger travel to remain the same. Having surprise jump ambushes is also very dramatic.
Since having large time-distance is not important to my universe to generate all those different worlds and their adventurousness (because it is ALL frontier past the core planets and the TC is very loosey-goosey), I don't care about the comms issue.
But I also didn't want humanity jumping across everywhere, so I have another limitation- can't jump unless the local gravitational/subspace anomalies are all charted.
That means an STL ship has to get to an area first, chart it (and keep the charts up afterwards), then jump back with the results before a system opens up.
SO I have scout cruisers- large STL ships that carry several Type S, a Frozen Watch and self-repair maintenance capability to first travel to the new frontier world.
Several issues with such a ship.
It has to carry enough life support for everyone to live for years, including the frozen watch. Since most of the distances involved are 1-2 parsecs, we are talking a LOT of supplies for 4-8 years (time dilation helps but more on that). Basically for CT prices 4 MCr per 10 people (the frozen watch normally won't count against that but we are talking about building in margins).
It has to be able to do maintenance. The Type S jump drives have to work once they get there so an unusually high capability and reliability has to be built in- and a lot of spare parts and fabs.
It has to survive frac-C travel. And being Traveller types, we don't do shields.
I had postulated a system subsumed in M-Drive and hull costs, deflectors. Idea is deflectors are a combination of mini-repulsors and fusion-based energized fields that can't stop lasers or missiles, but can deflect light particles/ionized gases.
Aramis then took us all through the numbers on particles in interstellar space, and when one is going frac-C the issue becomes not if but when you will impact. Arguably without special non-canon equipment it's suicide to run up anywhere near light speed.
So to keep my sanity and setting, I now say that those scout cruisers are maximum armored, have heavy extra deflectors, and keep a specialized sand cloud ahead of it to vaporize the vast majority of particles before they even approach the ship.
The fuel issue is not a factor for my setting. A key component has to do with lunar regolith being scraped up for He-3 for the first version of fusion, said lunar crust becomes the building blocks of a huge O'Neill cluster. So multi-year fusion reactors without the monthly fuel cost are normal, most of the fuel being carried is for accel/decel.
For reference, a couple of time dilation charts. Some people had said time stops at C and that's not quite the effect. I'm figuring something like .8C for my Scout Cruisers.