How to make good use of a small startup fund?
For those not familiar, Theoretical Computer Science is mostly formal mathematics. Thus the success patterns for research professors are nearly the same as those in Mathematics. In particular, research collaborations are critical.


  How can I use the (limited) funds that I have to benefit my career? 


There are ideas in two categories that can benefit your career: 1) build fruitful, productive research collaboration relationships; and 2) professional service in areas of critical need. (Nearly all tenure committees and funding agencies consider "service" or "broader impacts" as one of the major criteria for tenure or funding.)



EDIT: These ideas are unconventional and represent a particular set of values.  They value long-term benefits over short-term.  They value making a difference in the academic community over immediate personal benefit.  If you have different values, then you'd make different choices.



For the first category, you could use the funds to sponsor or host activities that will expand your research opportunities, especially build new collaborations.

For example, you could host a series of workshops that bring together researchers that don't normally work together.  These researchers could come from your department (if large), from other departments at your university, or from other universities.  Because you host the workshops, you can organize them to meet your objectives.  Maybe they are oriented toward a "challenge" (a la "hackathon"), or maybe oriented toward writing interdisciplinary research grant proposals,  or maybe you give each other tutorials on your specialties, hoping to find fruitful intersections.  For a good source of topic ideas, read the "Dear Colleague" letters from Program Mangers at NSF, and also the NSF program solicitations.

It may be there is already some workshop or conference that is close to your interests.  You could use your funds to host an add-on event.

For the category of professional service, you might consider these two ideas:


Host a series of workshops for CS majors at your university who are in under-represented groups (women, minorities). The goal of the workshop would be  help them with the personal, professional, and practical challenges they might face at your university.  If you don't know much about this topic, then you should recruit experts as presenters and facilitators.
Find your nearest Historically Black College (HBC) and co-host a Theoretical Computer Science workshop with someone in their CS department, aimed at students from both institutions.  You'd have to spend time to learn about the HBC, what their students are like, and how to usefully engage them in this topic.  In addition to benefits for the students, this could lead to an unexpected research collaboration for you.