I've a couple of thoughts. I've been following and studying SARS-CoV-2 since before the first case was "identified" in the United States, and have amassed a reasonable library of medical literature about it, COVID-19 diagnosis and treatment, and now, the vaccines. No advice you receive online should replace competent medical advice from a healthcare provider you know (and hopefully see professionally), but I can offer some thoughts.
In general, when I am asked this question, I respond that I can treat side effects and anaphylaxis successfully and fairly simply (of course, there are exceptions, but they are vanishingly few), but treating severe COVID-19 is much more questionable. The current vaccines (and I'm not sufficiently familiar with the data from Sinovax or Sputnic-V as their data are not readily available in a form I trust yet; this comment is thus limited to Pfizer/BioNTech, Moderna, Janssen/J+J, and AstraZenica) are either messenger RNA (mRNA) or recombinant DNA (rDNA) processes where proteins consistent with elements of the Spike protein are manually reproduced without culturing or utilizing live, attenuated or killed virus in the production. Thus, there is literally no way to contract COVID-19 from any of the vaccines.
The mRNA vaccines are encased in a lipid layer preventing the host immune system from responding to and destroying the encoding mRNA but allowing the mRNA to pair with ribosomes and have the host create the elements of the Spike protein that are released and seen as foreign material by the host immune system allowing creation of antibodies to the elements of that particular protein complex that can subsequently neutralize the ability of the coronavirus to attach to the acetylcholinesterase-2 receptors that are common in the mouth, nose, nasopharynx and other elements of the airway, as well as other communicating passages including the tear (lacrymal) ducts and corneal surfaces. These receptors, if the virus attaches to them, allow entry of the viral RNA material into the cell, and subsequent viral reproduction will create millions of infectious viral particles.
The primary mechanism of immunity seen so far, either by immunity conferred by infection or by vaccination, is that the antibodies prevent the Spike from attaching to the ACE2 receptor, usually by neutralizing the S1 protein. In addition, cellular immunity is recruited, where your innate immune system utilizes memory cells, CD4+ and CD8+ T lymphocytes, which respond to repeated exposure of antigens by initiating the predetermined immune response to the detected foreign material and initiating the response much faster than the first time one is exposed to the antigen naturally (or artificially with the vaccine).
Most reactions to the vaccines are relatively mild, and are considerably less intense than the result of infection with COVID-19 if you have a symptomatic case. Some people are asymtomatic, perhaps the majority, but they are not completely free from later complications. I'm including personal experiences for myself and my wife, as we both had bouts of COVID-19 and have also completed a full regimen of the Moderna vaccine. With COVID-19, my symptoms were present but mild enough to allow me to think they were associated with the high level of airborne allergens at the time, up to the time I lost my sense of taste and smell. The other clue was that none of my normal antihistamine treatments provided any relief. My wife had was met the criteria for moderate-to-severe symptoms and would have been hospitalized had I not been available to care for her. My symptoms lasted for about 4.5 days; hers lasted 14 days and she was debilitated for nearly 3 months thereafter, and has x-ray evidence of lung scarring.
By contrast, the side effects we had to the two shots of Moderna's mRNA vaccine were nearly identical: Lethargy for about 12 hours starting roughly 12 hours after the injection, and soreness at the injection site. I also experienced itching near the injection site for several days after the second injection. These are consistent with other vaccine injections such as influenza, shingles or pneumonia. Overall, significant reactions are rare and are on a level consistent with other vaccines. Quoting from https://jamanetwork.com/journals/jama/fullarticle/2777417:
Acute allergic reactions were reported by 2.10% overall, more frequently with the Moderna vaccine compared with Pfizer-BioNTech (2.20% [95% CI, 2.06%-2.35%] vs 1.95% [95% CI, 1.79%-2.13%]; P = .03). Anaphylaxis was confirmed in 0.025% (95% CI, 0.014%-0.040%): 0.027% from the Pfizer-BioNTech vaccine (95% CI, 0.011%-0.056%) and 0.023% from the Moderna vaccine (95% CI, 0.011%-0.044%) (P = .76).
Individuals with anaphylaxis were a mean (SD) age of 41 (13) years, and 15 (94%) were female; 63% had a prior allergy history and 31% had an anaphylaxis history. Mean time to anaphylaxis onset was 17 minutes (SD, 28; range, 1-120). One patient was admitted to intensive care, 9 (56%) received intramuscular epinephrine, and all recovered. Three employees, with prior anaphylaxis history, did not seek care.
The long-term effects of infection by SARS-CoV-2 are still being evaluated because the virus is relatively new, but have included long-term scarring to the lungs, clotting of peripheral vessels as well as clots migrating to the lung (pulmonary embolism) and increased clotting leading to stroke. In addition, cardiac anomalies have been seen including eosinophyllic infiltration of cardiac muscle, heart failure, shortness of breath, previously undiagnosed reactive airway disease, "brain fog", and loss of stamina. I'm sure there are others but I'm still coffee-deficient and only briefly looked at my literature cache. The US Centers for Disease Control has some good information: https://www.cdc.gov/coronavirus/2019-ncov/long-term-effects.html.
An additional concern is the rise of viral variants. These variations are normal. Viruses, especially coronaviruses mutate "all the time". The variants that do not promote virus genomic survival do not tend to survive: If the virus kills too many hosts then it can't replicate in additional hosts and that variant will die off with its hosts. On the other hand, a variant that is more infective, as we've been seeing with the so-called UK-, South African- Brazilian, and California-variants will tend to become more prevalent because they aren't killing a larger proportion of their victims but are recruiting new hosts.
Some news has cited that the various vaccines have reduced efficacy against the recent variants, but the conventional wisdom of virologists, epidemiologists and vaccinologists is that the current set of vaccines remains sufficiently effective against the known variants. In addition, because of how the mRNA and rDNA vaccines are made, updating them requires relatively minor modifications to the workflow, and much smaller studies and datasets for approval because the heavy work of proving safety and efficacy has been done.
About the only way to prevent another surge in cases involving the recognized (and over-hyped, in my opinion) variants is to increase the worldwide rate of vaccination, and to continue use of the simple and effective precautions including use of a 2-3 ply cloth mask (or even two masks), maintaining 2 meter social distancing, staying home if you don't feel completely well, and hand hygiene using soap and water or hand sanitizer based on 60% (ethanol) or higher sanitizers and the approved techniques for hand hygiene. Duration of handwashing or sanitizing matters. 20 seconds is the minimum to engage in effective hand cleaning, not the maximum.
So, if you've read all of this, the short answer is: Vaccination has some exceedingly minor risks, and the side effects generally do NOT rise to the level of symptoms and risks of COVID-19. My recommendation is to get vaccinated as soon as you can. One benefit is that the fewer susceptible persons out there, the fewer variant strains will infect people. Don't quibble over which vaccine you want, get the first of the approved vaccines available to you.
Self-isolate if you do not feel well