Would genital warts stop me joing armed forces?

Not a podiatry? Direct this to your family doctor.
Not necesarily. If there are only a few of them highly unlikely. If you have large plaques of warts impending your ability to run or do complex tasks then probably they will recommend treatment before enrollment. So I think you will be just fine:).

Related Questions

If I have genital warts will the outbreaks ever stop from happening? Or will I have outbreaks for the rest of my life?

"Warty" problem. Genital warts can be treated and removed so that they do NOT return. There are medications like Aldara, (imiquimod) Trichloroacetic acid (TCA) and an old one, Podophyllin that can be applied repetitively. Surgical options are Cryotherapy (freezing), lasering, and physical removal. Herpes, as a virus, tends to come back over and over again not the HPV (wart) virus. See a GYN MD for further advice.

Do genital warts go away and stop appearing? My nice bf (now ex) gave them to me and I was recently diagnosed with HPV this year. Depressed and angry

Yes if treated. See an on-gyn to, have these burns off. Laser treatments can eradicate the wart forever. Careful exam will be needed, and if your mate is infected, you can re contaminate the area.
Often go away. Often go away without treatment. Various treatments, none perfect. We can destroy the warts but not the virus, so they may return after any treatment. Imiquimod cream applied at home is standard prescription. Often several treatments are combined. The wart vaccine prevents infection by 4 (of many) HPV but has no effect on an established infection.

Does genital warts itch?

Possible. Warts in general do not itch. But in the genital area, they may become irritated and can be itchy. Please see a dermatologist or primary care doctor for evaluation to make sure there are no other reasons for the itch.