A few thoughts...
DOJ - they should be the one handling all of this. Biden did the correct thing in immediately and vocally distancing himself from his Attorney General pick (Merrick Garland), making clear its independence, as well as all the departments that answer to the AG (FBI, etc). They are starting now and making arrests based on various laws broken from evidence and data and this should continue after Biden takes office. They should also be the ones handling whether or not the rioters were incited by leaders and making similar actions based on clear evidence and data, not Congress (see below).
Congress - they should NOT be handling this, and this includes not going after Trump. His term is over in 10 days, and there is therefore no reason to further aggravate an already heated situation politically. Again, let the independent DOJ handle any necessary retribution and example-setting afterwards like any law enforcement agency would and should. Congress instead has a job to do on the 20th that they need to focus on, and that is to deal with the worsening COVID-19 and economic situation and heal the nation, and they need to get started on it right away, especially after the transition delays caused by Trump.
Capitol Police - based on videos, it appears to me that they responded in the correct manner. People were getting hurt in the front lines and it came to a point there really wasn’t any choice but to let them in and do their thing until backup arrived. The fault isn’t the Capitol Police. but the failure in leadership in preparation beforehand, namely the installation of more bodies such as the National Guard. This failure may have been purposeful, and heads should roll as a result, but it isn’t the Capitol Police.
Trump - He should just be allowed to sit and wallow in office until the 19th or until he chooses to beforehand if it’s earlier, to best taper the situation. Pelosi handled the threat of nuclear codes with the military and it is likely that any other reckless attempts of action at will be neutered instantly by those surrounding him, if not by a clearly shaken Trump himself. The only thing Trump may still do is pardon himself. Fine, let him. Federal charges should still occur if crimes were committed and at least we can then have an answer to the self-pardoning by the courts once they occur. If the Supreme Court says he can, who cares. By then, everyone will have moved on, except the crazy. And that group will get smaller and smaller each passing year. There is no way he will be re-elected now, even if he was allowed to run again. Besides, he likely will get charged for state crimes by New York and may be in jail in 2024 anyways even with the federal pardon.
Twitter - They are a private company and can do whatever the f*** they want in what’s posted on their platform. It isn’t censorship, by definition. They didn’t even need to provide an explanation.