There are several different programs that the Army currently offers. The caveat is that all or none may still be in place by the time you want to use them; it all depends on how many vets the Army has versus how many it needs.
The program I think you have heard of is one where you go to vet school, graduate, and then apply to join the Army as an active duty soldier (i.e. you work for the Army full-time). There may be various incentives available to get new vets to join. Right now there is a loan-repayment incentive which I think covers up to $150,000 in loans for a total seven-year commitment (at least three years active and four in the active Reserves). I am not absolutely sure on any of those numbers; for specific detail you will need to talk to a Army health care recruiter. Our local recruiter is Sergeant First Class Lindsay Dolly, 405-670-5958. Shes in OKC. I would encourage you to talk to her regarding specifics of these programs. However, recruiters exist to get people to join, so I would also suggest you not believe anything unless it is in a contract. J
There are also incentives which just pay you money directly rather than on your loans. The amount is less (the latest I have heard is $75,000 over 3 years) and the commitment is the same (3 yrs active, 4 Reserves).
There is also the Health Professions Scholarship Program (HPSP). This is a competitive application program that you can begin applying for as soon as you enter vet school (maybe even sooner? Ask SFC Dolly). It offers 1, 2 or 3 year scholarships that pay for your tuition, fees, books and a living stipend. The active-duty commitment begins as soon as you graduate and varies depending on the number of years of scholarships you received. This is very competitive, with only 24 scholarships per year being offered nationwide. It also requires that you spend 6 weeks a year during vet school (i.e. summers) at an Army post.
All of these programs require that you be an active duty soldier, in uniform. You would only be running a vet clinic part of the time. Army vets are also required to do a great deal of food inspection and food safety, manage/supervise soldiers and do public health activities as well as oversee the care of the Military Working Dogs. Running the vet clinic for soldiers pets is the lowest priority as far as the Army is concerned, and you may only be doing that ~25% of your time. If clinical practice is your goal, the Army is not going to provide it.
Joining the Reserves rather than active duty also has incentives. Last I heard they were similar, but for a total 7-year Reserve commitment (thats the one-weekend-a-month, 2-weeks-a-year, deploy every 5 years thing). That would allow you to pursue a civilian career if you wanted. However, you WOULD deploy at some point to a far-away place for 6 months to a year. This invariably occurs at the least convenient time for you. J
Finally, the Army does hire civilian vets. Theyre called NAF vets (non-appropriated funds) and help run their privately-owned animal vet clinics. However, there are no loan repayment incentives or anything for NAF vets.
Hopefully that answers at least some of your questions. I would recommend you talk to SFC Dolly about what exactly is available right now, then if you are still interested or have further questions you are always welcome to ask them of me. Good luck!