Conversion isn't always necessary if you are looking to make Aliyah. The political situation in Israel is such that the state has a separate definition of Jewishness from the Rabbinate. It gets complicated.
The state of Israel accepts Jewishness from both sides of the family. The Law of Return covers Jews of all types. If your father or grandfather was Jewish, you would be eligible for Aliyah regardless of whether your status is halachally valid. This is from when they amended the law in 1970.
The Law of Return
In 1970, Israel took another historic step by granting automatic
citizenship not only to Jews, but also to their non-Jewish children,
grandchildren, and spouses, and to the non-Jewish spouses of their
children and grandchildren. This addition not only ensured that
families would not be broken apart, but also promised a safe haven in
Israel for non-Jews subject to persecution because of their Jewish
The state simply requires evidence that your family is Jewish. This
can be evidence of affiliation with a specific Jewish community, a
bar/bat mitzvah, a death certificate or marriage certificate of
parents/grandparents which shows Jewishness, even a certified letter
from a Rabbi who has vetted your claim and verified your family
history as valid.
There are websites which list the required materials you would need.
Conversion is only necessary if you have no family history of Jewishness or if you seek to claim Jewish status once you have arrived in Israel. Israel operates under a "confessional" system which means that the state itself does not marry people through secular ceremonies. They only recognize marriages that have been conducted through a recognized religious community (Jewish/Christian/Muslim) or they recognize oversea marriages.
Many secular Israelis who hold no religious status actually take a plane ride over to Cyprus to get married and them come back to Israel. This is a loophole unaffiliated Israelis use to get married since the state offers no non-religious marriage process.
Assuming you actually do need to convert, you need to be sure that you are converting through a recognized and valid Jewish community. When I said that the political situation in Israel is complicated, this is what I mean. Certain conversions are not formally recognized. The Rabbinate actually has a blacklist of Rabbis who they don't recognize conversions from but they do not make this list public. If you contact an organization which works with converts who make Aliyah, they will likely have some names they can pass your way.
Besides that, there is currently a court ruling coming up which would force the state to decide whether Reform and Conservative conversions performed within the state are as valid. This ruling is actually decades in the making and may have an impact on your plans depending on how you choose to convert.
You have to make sure that you do your homework when you look for a Jewish community to convert into. The politics is weird on this and some communities simply are not accepted as legitimate.