We send hamsters. First in low powered exploratory launches, to prove that it can be done safely. Then high altitude launches, with triple stage rockets and compact video recorders inside and outside the passenger capsule. Rockets on this scale designed to carry delicate cargo (an egg) and return it safely to earth via parachute already exist, and one has been purchased for the project. It will be upgraded over time with higher power engines and additional stages, but until funding makes those upgrades possible, this will be the vessel which carries brave hamsternauts beyond the heavens:

But this is just stage 1 in Hamkind's conquest of space. The followup will be a space station. Or more accurately a skystation as obviously I lack the means to actually put hamsters in space. Nonetheless the design will closely resemble a futuristic space station, suspended by latex weather balloons and secured via a long fishing line tether to a heavy battery pack below which will not only anchor it against winds, but also keep it stable and upright, and supply power for the onboard resistive heating pad which the hamsters can use to warm themselves as needed if it becomes chilly:
