There is no prerequisite on levels. I have started a number of dogs in HRC seasoned from the get-go. You generally will need one more pass when you don't work your way through the levels. Started tests are very straightforward. They include two single retrieves on land and two on water. Dog must deliver within reach. All of this can be found in the HRC rulebook at the HRC website.
Most clubs have two separate hunts per weekend, so on a good weekend you can earn two passes. That can be at the same level or two different levels. For example, you could run started at one test, finish your SHR title and then run seasoned at the test the following day, or go from seasoned to finished. However, you cannot run two different levels at the test on the same day. Grab the rulebook off of the website. It covers the point system and what is expected at each level.
BTW, I just noticed that the Bryan/College station hunt test at the end of March is an Upland test only. The other hunts listed that month are normal HRC hunts with started, seasoned and finished levels. Upland tests are for finished retrievers and include quartering, being steady to wing and shot, and honoring another working dog.
I am a member of the Lone Star HRC in Dallas. We have a test earlier in March. It will be in Bonham, TX. Come on up if you can.