My apologies, @ronnoc32122. I hadn’t seen this ask when I responded to another ask concerning ghost-type starters. If I had, I would have responded sooner. In any case, when it comes to ghost-type options, you may wish to revisit that post here: http://bills-pokedex.tumblr.com/post/167247146514/bill-my-daughter-has-always-loved-ghost-type
From there, allow me to address your options for ice-types, as that’s a considerably shorter list. Considering your interest in water- and ghost-types, you may wish to look into options that overlap. For example, spheal is a very basic, easy-to-train pokémon that shares both the water and ice type, and because it’s both highly mobile and a native of tropical regions, it can adapt to inland battling in practically any climate. Lapras is a pokémon that meets similar criteria (water/ice, native to tropical regions, easy to train, extremely friendly), but despite being a formidable battler and an excellent partner, its inability to travel over land may make it less of an ideal partner in most regions besides ones where you’ll encounter plenty of water. (If you live in the Hoenn or Alola regions, however, I would highly recommend giving lapras a try!)
Alternatively, a few pokémon also evolve into ice-types or are ice-types that evolve into partial water- or ghost-types, namely seel, female snorunt, and shellder. Of these, snorunt tend to be the most popular, as they’re highly mobile and friendly, and they’re particularly powerful once they evolve into froslass. (Of course, even if you can’t find a dawn stone on your travels, keep in mind that snorunt’s other evolution, glalie, is still a fantastic partner.)
If, however, you don’t mind working with pokémon that aren’t partly water- or ghost-types, then this opens up your options a bit more. For example, you might also be able to consider cubchoo or vanillite, both of which are fantastically popular among ice trainers. (Cubchoo is cute but evolves into the powerful beartic, and vanillite is the first stage of a powerful three-stage evolution line that’s often underestimated by trainers.) Additionally, if you live in Alola, you may be able to get your hands on Alolan vulpix (a pure ice-type that evolves into the ethereal ice/fairy ninetales) or Alolan sandshrew (a sturdy ice/steel). Vulpix especially is highly intelligent and easy to train, but sandshrew is often seen as a stalwart partner capable of taking hits.
Meanwhile, those who live in Johto and Sinnoh have easier access to sneasel (mischievous and fickle but highly intelligent and loyal once you earn its trust) or smoochum (extremely intelligent but a bit difficult to train due to her lacking defensive capabilities). Swinub is also an excellent choice for those looking for a sturdy and easy-to-train pokémon (although it will eat you out of house and home, as a fair warning).
Really, just about the only ice-type pokémon I wouldn’t recommend is cryogonal, partly because it doesn’t thrive well outside of extremely cold environments and partly because it also often generates extremely cold environments in its surrounding area … which often doesn’t make one well-liked among trainers, wild pokémon, or neighbors.
As for water-types, that is a considerably longer list, which I may not be able to cover completely, I’m afraid. I can, however, say that all regions offer a traditional water-type starter. (Kanto has squirtle, Johto totodile, Hoenn mudkip, and so forth.) These are specially bred to be starters for new trainers, and thus, they often are perfectly balanced in terms of battling abilities, extremely intelligent and easy to train, and lacking in any sort of drawback that would make them excessively dangerous to handle. Above all other pokémon, I would recommend one of these as a starter.
Beyond that, though, the water type is a highly diverse classification of pokémon, and oftentimes, it comes down to what you look for in a partner and what’s most readily available to your region. (At least with ice-types, you will likely need to seek a breeder either way, as ice-types often live in areas too remote for a non-trainer to access.) For example, if you’re looking for an easy-to-train starter, pokémon such as marill, poliwag, buizel, panpour, and wingull are all wonderful choices. For strong pokémon, consider staryu, chinchou, frillish (also a partial-ghost), mareanie, or (if you have the patient for it) magikarp. And if you’re looking for unusual but reliable choices, consider bidoof (which evolves into the water-type bibarel) or lotad.
(As a note, I could also recommend a number of other pokémon, such as alolmomola, but oftentimes, the strongest water-types are strictly aquatic in nature and may be difficult to train on land. I only suggest magikarp because its Splash ability is far more versatile than one would initially assume, and using it for mobility may help it to evolve faster. Just be sure to treat it with an incredible amount of affection if you try this because otherwise, you may be on the receiving end of Twister shortly after your magikarp’s evolution.)
If all else fails, eevee evolves into the ice-type glaceon and the water-type vaporeon. I’m just saying.
Best of luck, good reader!