You can take your pick of cases, rimmed or rimless, just use the extractor for the case you choose. You can get into nit-piking or personal desires and attitudes which is smoke in the wind most of the time, when it comes to cartridges so just do your homework.
The 30-30 has been ran through the mill when it comes to rechambering and there are a ton of very good cases that have been used. For simplicity and component availability I would use a case that is readily available right now...7mm/8mm x 57 or resized '06, 444 Marlin, 450 Marlin, 303 British, 284, 348, to get that ever case length you want to clean up the chamber, and are all well known iterations on the 30-30 and right on up to the 450 NE#2.
Some are easier to do like the X 57, 303 Brit, '06, some a little bit harder, and some just plain tough, when it comes to case forming, and some are so close in case capacity it is hair splitting to pick one and say it is the "cats meow".
Some case capacities to consider.
307/308 53gr
x57/x57 IMP 54/60gr H2O
284 65gr
30-40 Krag/IMP 57/62 gr
30-444M 62 gr
30-348 79 gr
303 Brit/IMP 57/62 gr
405 Win 79gr
45-70 79gr
450M 78gr
45-90 91gr
450NE 135gr Now your talking!!!!!
And die costs have to be considered. The dies might cost more than the barrel and any excess neck length just gives you more room to seat the bullets out and get MORE case capacity, or gives you some freebore to play with. Hahahahahaha RCBS and Hornady might have dies already available for some of the more popular wildcats.
The 307/308 would be the quickest, cheapest and easiest to do with the 30-40 right along side and the dies are cheap and available. The 303 and x57 would be the next easiest.
As far as economy is concerned, because there is already a 308 Win barrel available it is a waste of money to do the 307/308 and 30-40 Krag I think. Plus unless you get a fairly large increase in ballistics it is economically a waste not to go for a bigger case and more pizzazz. I would definitely go for a case in the 80-100 gr range, but I like things on the narly side.
Then again a case in the 60-70 gr range would handle 90% of all North American game...30'06, 30-284, 30-444, one of the IMP cases.
The problem is lots of choices, lots of decisions. Be the first in your block to have a 30-405...
...or 30-45/125
Have fun deciding.
Luck