I have hiked from within the Basin to the South Rim but have never hiked into the Basin from the desert below. I understand we can hike in via Juniper Trail which seems to go directly to the South Rim or from Horace Wilson ( I think it is ) off Ross Maxwell Road. I would apprciate advice from anyone who has experience with these hikes. Thanks.
It is hard to tell from your question what you intend to do. Are you planning a day hike ending in the Basin? Do you plan to also go to the South Rim? Do you want to overnight on the South Rim or somewhere in the Chisos? Badknees is correct about coming in from Oak Spring via the Window, that would be the shortest route to the Basin (4.5 miles) with the least elevation gain (~1500').
If you want to go via the South Rim, then Blue Creek canyon from Homer Wilson ranch is easily accessed from the RMSD it is 8.0 miles to the South Rim at the Boot Canyon trail jct. with an elevation gain of 3100'. The beginning of that trail is a bit more work as it runs in the sandy wash and is harder walking with a steep switch backed climb at the end. It does have the red rocks and oaks in the bottom. If you are going straight to the Basin, not via the South Rim it would be 9.3 miles via Laguna Meadows.
Juniper Canyon of course starts with a high clearance drive to the trail head but is a firm trail all the way up and well switch backed. It has larger views of the surrounding area. It is 8.7 miles to the South Rim with almost 3300' elevation gain. If you are going straight to the Basin via Pinnacles it would be 11 miles.
Give us some more info and we can maybe give you some more ideas. Hope this helps.